**Unformatted text preview: **1/9/2021 Trigonometry Week 1 Test WEEK 1 TEST - SECTIONS 1.1 AND 1.4 ------- Take the Practice Tests, and then the Weekly Test
Trigonometry Week 1 Test - Grade Report
Score: 88% (88 of 100 pts) Submitted: Jan 9 at 2:28pm 1/26 1/9/2021 Trigonometry Week 1 Test
Question: 1 Grade: 1.0 / 4.0 Choose the table and graph of y
Select one table and one graph.
Choice 2
= −x −3. Selected x y −1 4 0 3 1 4 2 7 x y −1 −4 0 −3 1 −4 2 −7 x y −1 −2 0 −1 1 −4 2 −6 Points No Yes +1 No Yes +1 2/26 1/9/2021 Trigonometry Week 1 Test No No Solution Choose several values for x. Here, −1, 0, 1 and 2 are chosen. Substitute each x -value into the equation to find the corresponding y -value. x y y = 2
−x −3 −1 −4 y = −(−1) 0 −3 y = 2
−(0) −3 = −3 1 −4 y = 2
−(1) −3 = −4 2 −3 = −4 3/26 1/9/2021
2 Trigonometry Week 1 Test
−7 y = 2
−(2) −3 = −7 Plot each ordered pair from the table on a coordinate plane and then draw a line through the points. 4/26 1/9/2021 Trigonometry Week 1 Test
Question: 2 Grade: 1.0 / 4.0 Find both the x- and y- intercepts and the graph of y = 2
−3x −3x+6. Select the correct set of intercepts.
(1, 0), (−2, 0) and (0, 6) (50%) Select the correct graph. (50%) Solution Find the x -and y -intercepts.
x -intercept: y 0 = = x − 1 x y -intercept: y = Substitute 0 for y and solve for x. 2
−3x −3x+6 −3(x − 1) (x + 2) = = 0 1 or x + 2 or x = = The equation is quadratic, so solve by factoring. 0 −2 2
−3(0) −3(0)+6 = 6 Substitute 0 for x and solve for y. There are two x − intercepts, (1, 0) and (−2, 0) , and one y − intercept, (0, 6) .
Plot the x − and y − intercepts and then sketch a line through the intercepts. 5/26 1/9/2021 Trigonometry Week 1 Test Question: 3 If g(x)
g(5) = Grade: 1.0 / 4.0 6x − ∣ 3 + x ∣, find g(5) and g(−6). 22 (50%) = g(−6) = -39 (50%) Solution Evaluate the function for x = 5 g(5) = 30− ∣ 8 ∣ = = g(−6) 6(5) − |3 + (5)|
= So, g(5) 6(−6) − |3 + (−6)| = 22 and g(−6) Question: 4 = and x
= = −6.
30 − 8) −36− ∣ −3 ∣ = = 22 −36 − 3 = −39 −39. Grade: 1.0 / 4.0 Find the domain of the function.
f (x) = 5
x
9 (−∞, ∞) −
−
2
+ 3x
− √ 13 (100%) Solution Since the x -values of a polynomial function can be any real number, the domain of f is all real numbers, (−∞, ∞) . 6/26 1/9/2021 Trigonometry Week 1 Test
Question: 5 Grade: 1.0 / 4.0 If g (x) = 3x2 + 5x − 3 and f (x) = −2x2 −18x+7, find all real x -values such that g (x) = f (x) .
x = 2/5;-5 (100%)
If there are multiple solutions, separate the answers with semicolons (;). If the answer is not an integer, enter it as a fraction.
Solution g (x) = f (x) 2
3x
+ 5x − 3 = 2
−2x −18x+7 Substitute 3x2 2
5x +23x − 10 = 0 Move all the terms to one side and simplify. (5x − 2) (x + 5) = 0 Factor. or x + 5 5x − 2 x = So, If g (x) = 0 2 ∕ 5 = x 2
3x
+ 5x − 3 = = Set each factor equal to 0. 0 Solve each equation. −5 and f (x) for g (x) and −2x2 −18x+7 for f (x) . + 5x − 3 = 2
−2x −18x+7 then g (x) = f (x) when x = 2 ∕ 5 or x = −5. 7/26 1/9/2021 Trigonometry Week 1 Test
Question: 6 Grade: 1.0 / 4.0 True or false? The following is a graph of a function. Your response False Solution The graph fails the vertical line test. Therefore, this is not a function. 8/26 1/9/2021 Trigonometry Week 1 Test
Question: 7 Grade: 1.0 / 4.0 Choose the table and graph of y = 2+3x. Select one table and one graph.
Choice Selected x y −1 5 0 2 1 −1 2 −4 Points No No x y −1 −5 0 −2 1 5 2 4 No Yes +1 9/26 1/9/2021 Trigonometry Week 1 Test x y −1 −1 0 2 1 5 2 8 Yes +1 No Solution Choose several values for x. Here, −1,
x y y = 2+3x −1 −1 y = 2+3 (−1) 0 2 y = 2+3 (0) = 2 1 5 y = 2+3 (1) = 5 2 8 y = 2+3 (2) = 8 = 0, 1 and 2 are chosen. Substitute each x -value into the equation to find the corresponding y -value. −1 10/26 1/9/2021 Trigonometry Week 1 Test Plot each ordered pair from the table on a coordinate plane and then draw a line through the points. Question: 8 Grade: 1.0 / 4.0 Write the equation of a circle with center at (−4, 4) and radius 3 .
Your response (x+4) 2 + (y−4) 2 = 9 Solution Substitute r = 3, h = −4, 2
2
(x − (−4))
+ (y − (4)) Question: 9 and k = 2
(3) = 4 ⇒ into the equation of a circle with center at(h, k) ,
2
2
(x+4)
+ (y−4) = (x − h) 2 + (y − k) 2 2
= r , and simplify. 9 Grade: 1.0 / 4.0 True or false? The equation x2 − 6 + 6y 2 = 4 is a function. Your response false Solution Solve the equation for y
2
2
x
− 6 + 6y = 4 ⇒ 6y 2 = 2
4 − x
+ 6 ⇒ y 2 1
= 2
(10 − x ) 6 There are some x -values that will have two corresponding y -values, so x2 − 6 + 6y 2 = 4 is not a function. 11/26 1/9/2021 Trigonometry Week 1 Test
Question: 10 Grade: 1.0 / 4.0 Determine the distance between the two points (−1, −1) and (5, 7).
The distance between the points is 10 (100%)
Solution Substitute the coordinates from the ordered pairs (points) into the Distance Formula d
Let (x1 , y1 )
d = (−1, −1) and (x2 , y2 ) = (5, 7) −
−−−−−−−−−−−−−−−−−−−
2
2
= √(x
− x )
+ (y
− y )
2
1
2
1 and simplify. . = −
−−−−−−−−−−−−−−−−−−−−
√(5 − (−1))2 + (7 − (−1))2 Substitute. = −
−−−−−−−−
√(6)2 + (8)2 Simplify within the parentheses. = −
−−−−−
√ 36 + 64 Evaluate the powers. = −
−
−
√ 100 Add. = 10 Evaluate the square root. 12/26 1/9/2021 Trigonometry Week 1 Test
Question: 11 Grade: 1.0 / 4.0 Find both the x- and y- intercepts and the graph of 4x+2y = 6. Select the correct intercepts.
(0, 3 ) and ( 3
2 , 0) (50%) Select the correct graph. (50%) Solution Find the x - and y - intercepts.
x -intercept: y -intercept: 4x+2(0) 4(0)+2y = = 6 6 ⇒ ⇒ The x − and y − intercepts are (0, x = y = 3 ) 3
2
3 and ( Substitute 0 for y and solve for x.
Substitute 0 for x and solve for y. 3
2 , 0) . The equation is linear, so the graph forms a line. Plot the x − and y − intercepts and then sketch a line through the intercepts. 13/26 1/9/2021 Trigonometry Week 1 Test
Question: 12 Write x2 + y 2 Grade: 1.0 / 4.0 + 8x − 6y = 11 in the standard form of a circle and then identify the circle's center and radius. The standard form equation of the circle is
Your Answer:
Correct Answer: (x+4) (x+4) 2 2 + (y−3) + (y−3) 2 2 = 36 = 36 Your response Correct response Enter the center as an ordered pair, including the comma. Enter the center as an ordered pair, including the comma.
The center is at (-4,3) (100%)
The center is at (-4,3) Your response Correct response Enter the radius. Enter the radius. The radius is 6 (100%) The radius is 6 Solution Group the x-terms and the y-terms, and move the constant term to the right side.
2
2
(x
+ 8x) + (y
− 6y) = 11 Complete the square twice to write the x -terms as a perfect square trinomial and the y -terms as a perfect square trinomial.
2
2
(x +8x) + (y −6y) 2
2
(x +8x + 16) + (y −6y + 9) = = 11 Complete the square twice. 11 + 16 + 9 2
2
(x+4)
+ (y−3) The standard form equation is (x+4)2 = + (y−3) Factor each perfect square trinomial and simplify the right side. 36 2 = 36 , so the center is (−4, 3) and the radius is 6 . 14/26 1/9/2021 Trigonometry Week 1 Test
Question: 13 Grade: 1.0 / 4.0 Write the equation of a circle where A (1, 6) and B (3, 8) are the endpoints of a diameter.
Your response (x−2) 2 + (y−7) 2 = 2 Solution Find the radius r and the coordinates of the center (h, k) , then substitute those values into the standard form equation of a circle,
(x − h) 2 + (y − k) 2 2
= r . Use the Distance Formula to find the length of AB, the circle‘ s diameter, and divide the diameter by 2 to find the radius.
Then, use the Midpoint Formula to find the midpoint of AB, the circle‘s center.
For both formulas, let A (1, 6) be (x1 , y1 ) and B (3, 8) be (x2 , y2 ) . x1 = 1, x2 = 3, y1 = 6, y2 = 8
AB = −
−−−−−−−−−−−−−−−−−
√(1 − (3))2 + ((6) − 8)2 = √(−2)2 + (−2)2 = −−−−
√4 + 4 = –
√8 −
−−−−−−−−−−− So the radius is
center= ( –
√8
2 1+(3) Substitute r 2
= , –
= √ 2. 6+8
2 –
√ 2, h ) = (2, 7) = 2, and k = – 2
(√ 2) 2
2
(x − (2))
+ (y − (7)) = 7 ⇒ into the equation of a circle with center at (h, k) , (x − h) 2 + (y − k) 2 = 2
r , and simplify. 2
2
(x−2)
+ (y−7)
= 2 15/26 1/9/2021 Trigonometry Week 1 Test
Question: 14 Grade: 1.0 / 4.0 Find the domain of the function.
−
−−−−−−−
f (r) = √ −11r + 55 Your response (−∞, 5] Solution The domain of f is all real numbers except those r -values that make the radicand < 0. So, set the expression in the radicand ≥ 0 and solve for r.
−11r + 55 ≥ 0 ⇒ r ≤ 55
11 = 5 Reverse the inequality symbol when dividing by −11. The domain of f is all real numbers less than or equal to 5, (−∞, 5] 16/26 1/9/2021 Trigonometry Week 1 Test
Question: 15 Grade: 0.0 / 4.0 Use symmetry and intercepts to sketch the graph of y = ∣ 4x ∣ +2. Your response Solution Test the equation for each type of symmetry.
Respect to the x -Axis
−y y = = Respect to the y-Axis ∣ 4x ∣ +2 y − ∣ 4x ∣ −2 Not equivalent to y So, the graph of y = = y ∣ 4x ∣ +2. ∣ 4x ∣ +2 = = Respect to the Origin ∣ 4 (−x) ∣ +2 −y ∣ 4 (x) ∣ +2 y Equivalent to y = ∣ 4x ∣ +2. = = ∣ 4 (−x) ∣ +2 − ∣ 4 (x) ∣ −2 Not equivalent to y = ∣ 4x ∣ +2. is symmetric with respect to the y-axis. Find the intercepts.
x -intercept: 0 -intercept: y y = = ∣ 4x ∣ +2 ∣ 4(0) ∣ +2 ⇒ = no solution
2 Substitute 0 for y and solve for x .
Substitute 0 for x and simplify to find y. So, the graph does not cross the x -axis, and it crosses the y-axis at 2.
Find some additional points on the graph, on one side of the line of symmetry. Then, use the fact that for each (x, y) on a graph that is
symmetric with respect to the y-axis, (x, y) is also on the graph. Plot the points and sketch the graph. 17/26 1/9/2021 Trigonometry Week 1 Test Question: 16 Grade: 0.0 / 4.0 Find the domain of the function.
g (p) = p−5
2
p +3p−18 Your response (−6, 3) Solution The domain of g is all real numbers except those p - values that make the denominator =
solve for p.
2
p +3p − 18 = = −6 or So, set the expression in the denominator = 0 and 0 (p + 6) (p − 3) p 0 p = = 0 3 The domain of g is all real numbers except −6 and 3, R ∖ {−6, 3} . 18/26 1/9/2021 Trigonometry Week 1 Test
Question: 17 Grade: 1.0 / 4.0 If
F (x) = ⎧ 6
⎪ if x ≤ −10 ⎨ ∣5x − 6∣ if −10 < x < 6 if x ≥ 6 ⎩
⎪ find F
F
F 2
5x
+ 5 and F (12) .
(−10) = 6 (50%)
(12) = 725 (50%)
(−10) Solution Evaluate the function for x = −10 and x = 12
When x = −10, F (x) = 6. So, F (−10) = 6
When x
So, F = 12, F (x) (−10) = 6 Question: 18 = and F 2
5x
+ 5.
(12) = So, F 725 (12) = 2
5(12)
+ 5 = 725 . Grade: 0.0 / 4.0 is the midpoint between R(x, y) and S (4, 11).
Find the coordinates of R.
Enter the answer as an ordered pair, including the comma.
The coordinates of R are (1/2,7) (0%)
M (−3, 3) Solution Substitute the x -coordinate from the midpoint and the x -coordinate from S into the equation xM
−3 = x+4 −6 = x + 4 Multiply both sides by 2. −10 = x Subtract 4 from both sides. 2 = y+11 x +x
1
2
2 . Substitute. Substitute the y -coordinate from the midpoint and the y -coordinate from S into the equation yM
3 = = y +y
1
2
2 . Substitute. 2 6 = y + 11 Multiply both sides by 2. −5 = y Subtract 11 from both sides. 19/26 1/9/2021 Trigonometry Week 1 Test
Question: 19 Grade: 1.0 / 4.0 If
f (x) = 3
⎧
⎪ if x ≤ −8 ⎨ ∣2x − 3∣ if −8 < x < 7 if x ≥ 7 ⎩
⎪ 2x + 2 find f (7) and f (−12) .
f (7) = 16 (50%)
f (−12) = 3 (50%)
Solution Evaluate the function for x = 7 and x = −12.
When x = 7, f (x) = 2x + 2. So, f (7) = 2(7)
When x = −12, f (x) = 3. So, f (−12) = 3
So, f (7) = 16 and f (−12) = 3. Question: 20 + 2 = 16 Grade: 1.0 / 4.0 True or false? The equation x − 3 + 3y = 2 is a function. Your response true Solution Solve the equation for y
1
x − 3 + 3y = 2 ⇒ 3y = 2 − x + 3 ⇒ y = (5 − x )
3 Each x -value has one corresponding y -value, so x − 3 + 3y = 2 is a function. 20/26 1/9/2021 Trigonometry Week 1 Test
Question: 21 Grade: 1.0 / 4.0 Identify the type of symmetry, if any, for the graph of y = 5
6x . Your response Symmetric with respect to the origin Solution Test for symmetry with respect to the x -axis.
−y y 5
6x = 5
−6x = Substitute −y for y . Divide both sides by −1 to solve the equation for y . The equations are not equivalent, so the graph is not symmetric with respect to the x -axis.
Test for symmetry with respect to the y -axis.
y 5
6(−x) = y 5
−6x = Substitute −x for x . Simplify. The equations are not equivalent, so the graph is not symmetric with respect to the y -axis.
Test for symmetry with respect to the origin.
−y = 5
6(−x) Substitute −x for x and −y for y . −y = 5
−6x Simplify. y = 5
6x Divide both sides by −1 to solve the equation for y . The equations are equivalent, so the graph of y = 5
6x is symmetric with respect to the origin. 21/26 1/9/2021 Trigonometry Week 1 Test
Question: 22 Grade: 1.0 / 4.0 If w(x) = 6x2 − 2x, find w(3 + t).
Enter the expression in simplest form.
w(3 + t) 2
6t
+ 34t + 48 = (100%) Solution Evaluate the function for x
w(3 + t) = 3 + t. = 6(3 + t) = 6(3 + t) (3 + t) − 2(3 + t) = 6(9 + 6t + t = 54 + 36t + 6t = 6t So, w(3 + t) 2 2 − 2(3 + t) 2 ) − 2(3 + t) FOIL 2 Distribute. − 6 − 2t Combine the like terms +34t+48 = 6t 2 +34t+48 Question: 23 Expand the power. . Grade: 1.0 / 4.0 If g (x) = 4x2 +3x − 10, find all real x -values such that g (x) = 0.
If there are multiple solutions, separate the answers with semicolons (;). If an answer is not an integer, enter it as a fraction.
x = 5/4;-2 (100%)
Solution Substitute 0 for g (x) and solve for x. 4x − 5 x = = 0 = 2
4x +3x − 10 Substitute. 0 = (4x − 5) (x + 2) Factor. 0 or x + 2 Set each factor equal to 0. 5 ∕ 4 So, if g (x) = x = = 0 −2 2
4x +3x − 10, Solve each equation. then g (x) = 0 when x = 5 ∕ 4 or x = −2. 22/26 1/9/2021 Trigonometry Week 1 Test
Question: 24 Grade: 1.0 / 4.0 Identify the center, radius, and graph of (x − 3)2 2
+ (y + 3)
= 25. Your response Correct response Enter the center as an ordered pair, including the comma. Enter the center as an ordered pair, including the comma.
The center is at (3,-3) (100%).
The center is at (3,-3). Your response Correct response Enter the radius exactly. Do not use a decimal approximation. Enter the radius exactly. Do not use a decimal approximation.
The radius is 5 (100%). Select the graph of (x − 3)2 The radius is 5. + (y + 3) 2 = 25. Your Answer: Correct Answer: Solution From the equation, h = 3, k = −3, and r2 = 25, so r = 5. Therefore, the circle’s center is at (3, −3) and the radius is 5. Plot the points 5 units above, below, to the left and to the right of (3, −3) , and then sketch the circle through those points.
5 units above (3, −3) ⇒ (3, 2)
5 units below (3, −3)
units left of (3, −3) 5 units right of (3, −3) 5 ⇒ (3, −8) ⇒ (−2, −3) ⇒ (8, −3) 23/26 1/9/2021 Trigonometry Week 1 Test 24/26 1/9/2021 Trigonometry Week 1 Test
Question: 25 Grade: 1.0 / 4.0 If a person drives 370 miles at an average of 40 miles per hour, then their distance d from the destination (in miles) is a function of the number
of hours h driven.
Express this function as an equation, table, and graph. Your response The function's equation is d (h) Correct response
= 370 − 40h The function's equation is d (h) (100%) Your response The function can be represented by a table. = 370 − 40h Correct response The function can be represented by a table. h d (h) h d (h) 0 370 0 370 2 290 (50%) 2 290 5 170 (50%) 5 170 Select the correct graph for d (h) Your Answer: Correct Answer: 25/26 1/9/2021 Trigonometry Week 1 Test Solution The distance traveled after h hours is 40h. So, the distance d from the destination, which is 370 miles at h
Choose appropriate values for h and substitute into the equation to find the ordered pairs for the table.
d (0) = 370 − 40 (0) = 370 d (2) = 370 − 40 (2) = 290 d (5) = 370 − 40 (5) = 170 = 0, is d (h) = 370 − 40h. So, a corresponding table is
h d (h) 0 370 2 290 5 170 The equation d (h) = 370 − 40h describes a line with slope −40 and y -intercept 370. 26/26 ...

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