Mac 1140 Review

Review for test 1

1)

Find f(x + 1) when f(x) = 4x2 - 2x + 5.

2) Find f(2x) when f(x) = 2x2 - 3x + 2.

Identify the intervals where the function is changing as requested.

3) Decreasing

4) Increasing

5) Use the graph of the function f, given below, to sketch the graph of the given function g(x) = -f(x + 2) + 2. Use the

transformations. Do one transformation at a time.

6) Determine whether or not the graph below is the graph of a function of x. Explain.

7) Determine whether or not the graph below is the graph of a function of x. Explain.

A graph of y = f(x) is given . No formula for f is given. Graph the given equation.

8)

y = f(x)

y = f(2x)

9)

10)

y = f(x)

y = f(x)

y = -2f(x + 1) - 3

y = 2f(x)

11) Write the formula for the piecewise function whose graph is given below.

12) Function f is given below. Find f(-4) .

3x  2



f ( x)   x

2 x  1



f o r x  2

for

2 x 3

for

x3

13) Determine whether the function f(x) = x3 +3x2

is even, odd, or neither.

14) Let f(x) = 7 , and g(x) = 4 . Find (fog)(x)

x8

5x

15) Find the x- and y-intercepts of f(x) = -x2(x+5) (x2+3)

16) Graph f(x) = (x+3)3 -4 to determine whether f is a one-to-one function. If it is, find its inverse.

17) How can the graph of f(x) = -(x-2)2 + 3 be obtained from the graph of y = x2? List the transformations in the correct

order.

18) Find the inverse of the given function. Justify why the inverse exists.

a) f(x) = 3x2 -6, x  0

b) f ( x)  2 x  1

3  5x

19) Find functions f and g so that h(x) = (f og)(x) where h(x) =

1

2x  1

20) The graph of the function f is shown below. Graph, using transformations, g(x) = f(-x) + 3

21) Determine the domain and range of the function.

22) For the function f(x) = 3 , construct and simplify the difference quotient f ( x  h)  f ( x) .

x 5

23) Given

f ( x) 

h

2 Find the domain of the composite function f og.

2 and

g ( x) 

3x  1

x

24)...