EC 3 Review

Inverse Functions

100

The inverse of a function f is denoted by _____.

f^-1

200

What is the inverse of log?

Exponential

300

What is the inverse of the function y = (2/5)x +5

y = (5/2)x - (25/2)

400

Given the function 𝑓(𝑥) = 3𝑥² + 1, find the inverse of 𝑓(𝑥).

f^-1(x) = √ ((𝑥−1)/3)

500

What is the inverse of the function y = log(x - 4)?

𝑦 = 10^x + 4

Inverse on Tables/Graphs

100

Finding the inverse on tables and graphs are the same in that you have to switch the ___ and ____ to find the solution.

x and y

200

If f and g are inverses of each other, then:
The domain of f is the same set as the ______ of g
The range of f is the same set as the _______ of g

range

domain

300

The graphs are _______ of one another across the line y = x.

reflections

400

What line do you draw to create the inverse graph?

y = x

500

If you were given a graph, how would you find the domain and range of it's inverse?

Find the domain and range of the original graph and switch them

Rational Function Key Features

100

What number can you not divide by?

Zero

200

What is an x-intercept?

It is where the graph crosses the x axis

300

For which value(s) of x is the function f(x) = (x² - 16)/(x + 5) undefined?

x = -5

400

What is the horizontal asymptote of f(x) = 1/(x² - 9)? Explain.

y = 0 because the denominator has the higher power

500

Given: f(x)=(x + 7)/(x² + 2x - 3) determine the vertical asymptote(s) for f(x).

x = 1 and x = -3

Transforming Rational Functions

100

Which letter determines if your graph shifts left or right?

c

200

What type of shift happens when a is negative?

The graph shifts down

300

Identify a, b, and c for the following rational function: f(x) = -(2/x+5) + 3

a = 3

b = -2

c = -5

400

Let f(x)=1/x and g(x)=1/(x - 3). Describe the transformation from f(x) to g(x).

translated 3 units to the right

500

If the function y=1/(x-a) is shifted b units to the left and c units down, what would the new function be?  

(1/(x - a + b)) - c