Solved by Expert Tutors
Solved by Expert Tutors
Question

I have two problems that I need solved. They are the following: y=-2x^2+3 and y=2√x +1


I am attaching the teacher's example. Here are the instructions:
There are many ways to go about solving math problems. For this assignment you will be required to do some work that will not be included in the discussion. First, you need to graph your functions so you can clearly describe the graphs in your discussion. Your graph itself is not required in your post, although the discussion of the graph is required. Make sure you have at least five points for each equation to graph. Show all math work for finding the points.
Specifically mention any key points on the graphs, including intercepts, vertex, or start/end points. (Points with decimal values need not be listed, as they might be found in a square root function. Stick to integer value points.)
Discuss the general shape and location of each of your graphs.
State the domain and range for each of your equations. Write them in interval notation.
State whether each of the equations is a function or not giving your reasons for the answer.

Select one of your graphs and assume it has been shifted three units upward and four units to the left. Discuss how this transformation affects the equation by rewriting the equation to incorporate those numbers.
Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing the thought behind your math work.):
Function Relation
Vertical Line test Transformation

INSTRUCTOR GUIDANCE EXAMPLE: Week Five Discussion Relations and Functions pg 709 #31 The relation is f ( x ) = √( x – 1) where the -1 is included with x under the radical. f (1) = √(1 – 1) = √0 = 0 f (5) = √(5 – 1) = √4 = 2 f (5/4) = √(5/4 – 1) = √(¼) = ½ f (10) = √(10 – 1) = √9 = 3 f (2) = √(2 – 1) = √1 = 1 x f ( x ) = √( x – 1) 1 0 5/4 ½ 2 1 5 2 10 3 This being the graph of a square root function , it is shaped like half of a parabola laid over on its side. It has a starting point at (1, 0) and extends infinitely in the positive infinity direction (to the right). This graph falls entirely in the first quadrant and doesn’t exist in any of the other three quadrants. This function has no y intercepts and the only x intercept is the same as its starting point at (1, 0). I chose my x values carefully so that the y values were rational numbers coming out of the radical. The domain is all real numbers greater than or equal to 1, while the range is all non-negative real numbers. In interval notation it is written as follows: D = [1, ) and R = [0, ) This relation is a function because every element of the domain has one and only one value associated with it in the range , and it passes the vertical line test. pg711 #57 The relation is f ( x ) = 1 - | x | where the 1 and the subtraction are outside of the absolute value bars. f (-4) = 1 - |-4| = 1 – 4 = -3 f (1) = 1 - |1| = 1 – 1 = 0 f (-1) = 1 - |-1| = 1 – 1 = 0 f (4) = 1 - |4| = 1 – 4 = -3 f (0) = 1 - |0| = 1 – 0 = 1 x f ( x ) = 1 - | x | -4 -3 -1 0 0 1 1 0 4 -3 This is the graph of an absolute value function so it is shaped like a straight sided V with a sharp turn at the vertex. The a value is negative and so the V opens downward. The majority of the graph occurs in the third and fourth quadrants with only a tiny bit crossing into the first and second quadrants.
Background image of page 1
The highest point on the graph occurs at the vertex, (0, 1) and the graph is symmetrical across the y-axis. The y-intercept is at the vertex (0, 1) as well, and the x intercepts are at (-1, 0) and (1, 0). The domain is all real numbers while the range is restricted to real numbers less than or equal to 1. This relation is also a function because it passes the vertical line test, and each domain value has one and only one range value associated with it. Let us take this same function and shift it three units upwards and 4 units to the left. How will this affect the equation? Three units upwards means we add a positive 3 outside of the absolute value bars. Four units to the left means we add a positive 4 inside of the absolute value bars. The function will now look like this: f ( x ) = 1 + 3 – | x + 4| so f ( x ) = 4 – | x + 4| and this reflects a transformation of the function three units up and four units to the left. Just for the sake of a thorough example I am also going to show the other function transformed in the same manner. Three units upwards means we add a positive 3 outside of the radical. Four units to the left means we add a positive 4 inside of the radical. The function will now look like this: f ( x ) = 3 + √( x – 1 + 4) so f ( x ) = 3 + √( x + 3) This does incorporate the two shifts into the transformed function.
Background image of page 2
Sign up to view the entire interaction

Step-by-step answer

s a mole

gue vel laoreet ac, dictum vitae odio. Donec aliquet. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nam lacinia pulvinar tortor nec facilisis. Pellentesque dapibus efficitur laoreet. Nam risus ante, dapibus a molestie consequat, ultrices ac magna. Fusce dui lectus, congue vel laoreet ac, dictum vitae odio. Don

week 5.docx
lestie c llentesque dapibus eff , mo it e sque dap su e s e s a molestie consequat, ultrices ac magna. Fusce dui lectus, congue vel laoreet ac, dictum a. Fu consectetur adipiscing elit. Nam lacinia

Subscribe to view the full answer

Subject: College Algebra, Math

Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.

  • -

    Study Documents

    Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

    Browse Documents
  • -

    Question & Answers

    Get one-on-one homework help from our expert tutors—available online 24/7. Ask your own questions or browse existing Q&A threads. Satisfaction guaranteed!

    Ask a Question
Let our 24/7 College Algebra tutors help you get unstuck! Ask your first question.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes