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Operations with Functions Worksheet

NAME

For Problems 1­4, use f ( x) = 2 x 2 - 5 and g ( x) = x 2 - 3 x + 1 to find the indicated values. 1. (f + g)(1) 2. (f ­ g)(­2) 4. (f ÷ g)(1.5)

3. (fg)(4)

For Problems 5­8, use the functions f ( x) =

x +1 x+2 , g ( x) = to find and simplify: x -3 x+3 6. (f - g)(x)

5. (f + g)(x)

7. (fg)(x)

8. (f ÷ g)(x)

For Problem 9, use the table definitions of H(t) and r(t) shown below to find the indicated operation.

t H(t)

1.0 4.8

1.5 2.6

2.0 0.9

2.5 3.0 3.5 ­0.2 ­1.4 ­3.3

t r(t)

1.0 1.2

1.5 2.0 2.5 ­2.5 ­5.0 ­3.8

3.0 0.5

3.5 7.4

9. (a) (r + H)(2.5) (c) (r ­ H)(2.0) (e) (rH)(1.5) (g) (r ÷ H)(1.0)

(b) (r + H)(1.0) (d) (H ­ r)(3.0) (f) (rH) (3.5) (h) (r ÷ H)(2.5)

Problem 10 refers to the graphs of f(x) and g(x) shown.

3

f(x) f

3

g g(x)

-3

3

-3

3

-3

-3

10. Find the indicated value. (a) (f + g)(1) (c) (fg)(2)

(b) (f ­ g)(­1) (d) (f ÷ g)(­3)

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