# EVALUATING COMPOSITE FUNCTIONS FROM GRAPHS WORKSHEET

Problem 1 :

The first of the two graphs shows two functions ๐ ๐๐๐ ๐. The second shows two functions โ ๐๐๐ ๐. Use the graphs to compute the following:

 1) (๐ โฆ ๐)(โ4) = 2)  (๐ โฆ ๐)(3) =3) (๐ โฆ ๐)(โ2) =4) (๐ โฆ ๐)(3) =5) (๐ โฆ ๐)(โ5) =6) (๐ โฆ ๐)(โ3) =7) (โ โฆ ๐)(0) = 8) (โ โฆ ๐)(โ1) =9) (โ โฆ ๐)(2) = 10) (โ โฆ ๐)(โ3) =11) (๐ โฆ โ)(0) = 12) (๐ โฆ โ)(2) = 13) (๐ โฆ โ)(โ4) =14) (๐ โฆ โ)(โ2) =

Solution

Problem 2 :

Refer to the graph to complete the statements below.

a) (f + g)(-3) = ______

b) (f ยท g)(2) = ______

c) (f/g)(-1) = ______

d) (f โ g)(3) = ______

e) g-1(-4) = ______

f) Evaluate (f โ f)(2) ______

g) Evaluate g(f(g(1))) ______

h) State the domain of f + g _____

i) State the domain of f/g. ______

j) Evaluate (f(3))3 - 4g(-2) ______

k) For what value(s) is f(x) = 3? _______

Solution

## Answer Key

1) (๐ โฆ ๐)(โ4) = -3

2)  (๐ โฆ ๐)(3) = f[g(3)] = f[0] ==> 2

3) (๐ โฆ ๐)(โ2) = f[f(-2)] = f[3] ==> 1

4) (๐ โฆ ๐)(3) = g[g(3)] = g[0] ==> -3

5) (๐ โฆ ๐)(โ5) = g[f(-5)] = g[-3] ==> -5

6) (๐ โฆ ๐)(โ3) = g[f(-3)] = g[1.5] ==> -1.5

7) (โ โฆ ๐)(0) = h[k(0)] = h[4] ==>  4

8) (โ โฆ ๐)(โ1) = h[k(-1)] = h[3] ==> 3.5

9) (โ โฆ ๐)(2) = h[k(2)] = h[0] ==> 2

10) (โ โฆ ๐)(โ3) = h[k(-3)] = h[-5] ==> -0.5

11) (๐ โฆ โ)(0) = k[h(0)] = k[2] ==> 0

12) (๐ โฆ โ)(2) = k[h(2)] = k[3] ==> -5

13) (๐ โฆ โ)(โ4) = k[h(-4)] = k[0] ==> 4

14) (๐ โฆ โ)(โ2) = k[h(-2)] = k[1] ==> 3

2)  a)(f + g)(-3)  = -1

b)  (f ยท g)(2) = 0

c)  (f/g)(-1) = 2/(-3)

d)  (f โ g)(3) = 4

e)  x = -3

f) (f โ f)(2) = 2

g)  g(f(g(1))) = 0

h)  the domain of (f + g)(x) is [-3, 4].

i)  domain of (f/g)(x) = [-3, 1] u (3, 4]

k) (f(3))3 - 4g(-2) = 24

l)   x values are -2, 0 and 2.

## Recent Articles

1. ### Finding Range of Values Inequality Problems

May 21, 24 08:51 PM

Finding Range of Values Inequality Problems

Read More

2. ### Solving Two Step Inequality Word Problems

May 21, 24 08:51 AM

Solving Two Step Inequality Word Problems

Read More

3. ### Exponential Function Context and Data Modeling

May 20, 24 10:45 PM

Exponential Function Context and Data Modeling

Read More