topic badge
CanadaON
Grade 12

Graphs of Composite Functions

Interactive practice questions

Consider the functions $f\left(x\right)=2x$f(x)=2x and $g\left(x\right)=4$g(x)=4.

a

If $y$y is defined as $y=f\left(x\right)+g\left(x\right)$y=f(x)+g(x), state the equation for $y$y.

b

Use the given graphs of $f\left(x\right)$f(x) and $g\left(x\right)$g(x) to graph the function $y$y.

Loading Graph...
c

What transformation of $f\left(x\right)$f(x) does $y$y correspond to?

A vertical translation $4$4 units down.

A

A vertical dilation by a factor of $\frac{1}{4}$14.

B

A vertical dilation by a factor of $4$4.

C

A vertical translation $4$4 units up.

D
Easy
1min

A function $y$y is defined as $y=f\left(x\right)-g\left(x\right)$y=f(x)g(x).

Easy
6min

Consider the following expression: $\frac{x^2-2x-8}{x+2}$x22x8x+2

Easy
2min

Consider the rational expression: $\frac{x^2-5x+6}{x^2+2x-8}$x25x+6x2+2x8

Easy
2min
Sign up to access Practice Questions
Get full access to our content with a Mathspace account

Outcomes

12F.D.2.4

Determine the composition of two functions [i.e., f(g(x))] numerically (i.e., by using a table of values) and graphically, with technology, for functions represented in a variety of ways, and interpret the composition of two functions in real-world applications

12F.D.2.5

Determine algebraically the composition of two functions [i.e., f(g(x))], verify that f(g(x)) is not always equal to g( f(x)) and state the domain and the range of the composition of two functions

12F.D.2.6

Solve problems involving the composition of two functions, including problems arising from real-world applications

What is Mathspace

About Mathspace