Functions and Transformations Assignment

Consider a rectangle with width of x units and an area of 10 square units. The length l of the rectangle can be modeled by the function . Suppose the width of the rectangle increases 1 unit, while the area remains constant. Which graph models the length of the new rectangle?

C

Which is the graph of an odd function?

D

Which describes the transformations of y = f(x) that would result in the graph of y = f(-x) - 7.

a reflection in the y-axis followed by a translation down by 7 units

Function f undergoes two transformations to become g. Express g(x) in terms of f(x).

g(x) = - f(x - 2)

Given f(x) = log2x, which of the functions below represents g(x) resulting from reflecting the graph of f(x) in the x-axis and shifting left by 2 units?

g(x) = -log2(x + 2)

The temperature in Fahrenheit, x, is converted into the temperature in Celsius with the formula, . The graph for this formula is provided:

horizontal translation vertical compression

The function g(x) = 3x3 + x is an odd function. Which transformations of g(x) would result in odd functions? Check all that apply.

-g(x) g(2x) g(-x)

Given the graphs of y = f(x) and y = g(x), g(x) = f(x) + expresses g(x) in terms of f(x).

3

Which is the graph of ?

B

Eileen is trying to test if the function f(x) = x2 + 2x + 5 is even, odd or neither. She produces the following work: f(- x) = (-x)2 + 2(-x) + 5 = x2 - 2term-1x + 5 What conclusion can she reach?

f(x) is neither