{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

sample_midterm-2

# sample_midterm-2 - (b f x = 1 x 2 − 4 x 3 6 Sketch the...

This preview shows pages 1–7. Sign up to view the full content.

Mathematical Functions Sample Midterm Exam In the following problems you are required to show all your work and provide the necessary explana- tions everywhere to get full credit. 1. Find all real solutions of the following equations: (a) x 2 3 x 8 = 0 (b) x + 1 x 2 = x + 1 (c) x 1 / 3 3 x 1 / 6 + 2 = 0

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2. Solve the following inequalities. Express the solutions using interval notation and graph the solution sets. (a) x 2 + x 12 (b) x + 2 2( x 3) > x 1 (c) | 2 x 1 | > 1
3. Helen earns \$8 . 00 per hour at her job, but if she works more than 35 hours in a week she is paid 1 1 2 times her regular wage for the overtime hours worked. One week her gross pay was \$400 . 00 . How many overtime hours did she work that week? 4. Find an equation of the line through the points (3 , 2) and ( 1 , 4) .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
5. Find the domain of the following functions. Express the solutions using interval notation . (a) f ( x ) = ( x 1)( x + 2)( x + 4)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (b) f ( x ) = 1 x 2 − 4 x + 3 6. Sketch the graph of the piecewise deﬁned function f ( x ) = x 2 if x < 1 x 3 if x ≥ 1 and ﬁnd f (0) , f (1) , f (2) . 7. Sketch the graph of the function f ( x ) = −| x − 1 | + 2 , not by plotting points, but by starting with the graph of a standard function and applying transformations. 8. Show that the equation x 2 + y 2 + 8 x − 4 y + 3 = 0 represents a circle, and ﬁnd the center and radius of the circle. 9. Find the maximum or minimum value of the function y = x 2 − 2 x + 2 . 10. Use f ( x ) = √ 1 − x and g ( x ) = 1 x 2 + 1 to ﬁnd (a) f ◦ g (b) g ◦ f (c) f ◦ f (d) g ◦ g (e) fg (f) f/g 11. Find the inverse of the following functions: (a) f ( x ) = x x − 2 (b) f ( x ) = 1 + 2 x 3...
View Full Document

{[ snackBarMessage ]}

### Page1 / 7

sample_midterm-2 - (b f x = 1 x 2 − 4 x 3 6 Sketch the...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online