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Practice with Functions

I need some help to push me through with functions. (Please see the Attached Questions File)

5. Perform the requested operation or operations.
f(x) = 2x - 9, g(x) = 4x - 4

Find (f - g)(x)
Answer. -2x - 5

6. Compare the graph of the given quadratic function f with the graph of y = x2
f(x) = (x - 8)2 + 4
Answer. a translation 8 units right and 4 units up

Solve the problem
Find (f ° g)(3) when f(x) = -5x + 2 and g(x) = 8x2 + 9x + 7
Answer: -528

8. Compute and simplify the difference quotient
f(x + h) - f(x)
H
, h ≠ 0.

Answer: 4
10. Consider the function h as defined. Find functions f and g so that (f ° g)(x) = h(x).
h(x) = 10/x^2 +4
answer. f(x) = x + 4, g(x) = 10/x^2

11. Solve the problem.
Find (f °g)(-6) when f(x) = 4x + 4 and g(x) = 6x2 - 3x - 6.
Answer: 916

13. Determine whether or not the function is one-to-one.

15. Perform the requested operation or operations.
f(x) = 9x - 4, g(x) = 6x - 6
Find (f - g)(x).
Answer: 3x + 2
16. Graph the basic function using a solid line and the transformed function using a dotted line.
y = -3 |x|

20. Solve the problem
Select the equation that describes the graph shown

A. y = (x + 2)2- 4
B. y = (x + 4)2 + 2
C. y = (x - 4)2 + 2
D. y = x2 - 4

Attachments

Solution Preview

The solution file is attached.

5. Perform the requested operation or operations.
f(x) = 2x - 9, g(x) = 4x - 4

Find (f - g)(x)

(f - g)(-x) = 2x - 9 - (4x - 4) = 2x - 9 - 4x + 4 = -2x - 5

Answer. -2x - 5

6. Compare the graph of the given quadratic function f with the graph of y = x2
f(x) = (x - 8)2 + 4

.
Answer. a translation 8 units right and 4 units up (This answer is correct!)

Solve the problem
Find (f ° g)(3) when f(x) = -5x + 2 and g(x) = 8x2 + 9x + 7

(f O ...

Solution Summary

Neat and Step-by-step Solutions to all questions. Graphs (if any) are also included.

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