Question

1.Match each function h with the transformation it represents, where c > 0a.A vertical shift of f, c units downb.A vertical shift of f, c units upc.A horizontal shift of f, c units to the rightd.A horizontal shift of f, c units to the lefth(x)=f(x)-ch(x)=f(x)+ch(x)=f(x+c)h(x)=f(x-c)2. Find (f/g)(x) for f(x)=1/x and g(x)=x^33. find (fg)(x), where f(x)=2x-5 and g(x)=2-x4. Given f(x)=x+2 and g(x)=4-x^2 find the following (f o g)(x)5.Given f(x)=x+2 and g(x)=4-x^2 find the following (g o f)(x)6. True or False.A function is one-to-one when each value of the dependent variable corresponds to exactly one value of the independent variable.7.The number of pounds of apples a cannery can process and the processing cost are P(h) = 375h and C(n) = 0.35n + 1000 where P(h) is the number of pounds of apples that can be processed in h hours and C(n) is the cost of processing n pounds of apples. Use composition of functions to find the cost of operating the cannery 32 hours. Be sure to show all of your work and the composed function you used.8. Find the inverse of the following function. Be sure to show all of your work.f(x)=2x^3+19.Verify that f and g are inverse functions algebraically. Show all your work.f(x)=7x+1 and g(x)=x-1/710. True or False.The following function has an inverse.f(x)=-3x-7

Answer 1

1. Match:

a.

A vertical shift of f, c units down

The answer is, h(x)=f(x)-c.

b.

A vertical shift of f, c units up

The answer is, h(x)=f(x)+c.

c.

A horizontal shift of f, c units to the right

The answer is, h(x)=f(x-c).

d.

A horizontal shift of f, c units to the left

The answer is, h(x)=f(x+c).