1.
Determine whether the graph is the graph of a function. (1 point)
A coordinate axis is drawn with an exponential curve crossing the y axis at one increasing towards infinity.

Yes

No
2.
Determine the domain of the function. (1 point)
f as a function of x is equal to four divided by x squared.

x ≥ 0

All real numbers except 0

All real numbers except 3

All real numbers
3.
Find the range of the function.
f(x) = (x - 2)2 + 2 (1 point)

All real numbers

y ≥ 0

y < 2

y ≥ 2
4.
Determine the domain of the function. (1 point)
f as a function of x is equal to the square root of seven plus x.

x ≥ 0

All real numbers

x ≥ -7

x > 0
5.
Determine the intervals on which the function is increasing, decreasing, and constant. (1 point)
A cube root graph is shown crossing the y axis at -5.

Increasing on x < 0; Decreasing on x > 0

Increasing on x > 0; Decreasing on x < 0

Increasing on all real numbers

Decreasing on all real numbers
6.
Estimate graphically the local maximum and local minimum of f(x) = 4x2 + 3x + 2. (1 point)

Local maximum: (-0.4,1.44); local minimum: (0,-0.37)

Local maximum: (-0.4,1.44); no local minimum

No local maximum; local minimum: (-0.4,1.44)

No local maximum; local minimum: (0,-0.37)
7.
Determine if the following function is even, odd, or neither.
f(x) = -9x4 + 5x + 3 (1 point)

Odd

Even

Neither
8.
f(x) = 3x + 6, g(x) = 2x2
Find (fg)(x). (1 point)

2x2 + 3x + 6

6x + 12

6x2 + 12x

6x3 + 12x2
9.
f(x) = Square root of quantity three x plus seven. , g(x) = Square root of quantity three x minus seven.
Find (f + g)(x). (1 point)

Square root of six x.

x Square root of six.

3x

Square root of quantity three x plus seven. + Square root of quantity three x minus seven.
10.
f(x) = x2 + 3; g(x) = Square root of quantity x minus two.
Find f(g(x)). (1 point)

f(g(x)) = (x2 + 3)( Square root of quantity x minus two. )

f(g(x)) = Square root of quantity x minus two divided by quantity x squared plus three.

f(g(x)) = x + 1

f(g(x)) = Square root of quantity x squared plus three.
11.
Find f(x) and g(x) so that the function can be described as y = f(g(x)). (1 point)

y = Four divided by x squared. + 9

f(x) = x + 9, g(x) = Four divided by x squared.

f(x) = x, g(x) = Four divided by x. + 9

f(x) = One divided by x. , g(x) = Four divided by x. + 9

f(x) = Four divided by x squared. , g(x) = 9
12.
Find the inverse of the function.
f(x) = 3x - 2 (1 point)

f-1(x) = Quantity x plus two divided by three.

f-1(x) = x divided by three + 2

f-1(x) = Quantity x minus two divided by three.

Not a one-to-one function
13.
Find the inverse of the function.
f(x) = x3 + 4 (1 point)

f-1(x) = -4 Cube root of x.

f-1(x) = Cube root of quantity x minus four.

f-1(x) = Cube root of quantity x plus four.

Not a one-to-one function
14.
Find the inverse of the function.
f(x) = 6x3 - 3 (1 point)

f-1(x) = Cube root of quantity x minus three divided by six.

f-1(x) = Cube root of quantity x plus three divided by six.

f-1(x) = Cube root of quantity x divided by six. + 3

Not a one-to-one function
15.
Determine if the function is one-to-one. (1 point)
A graph is shown of two curves increasing connecting at the point 0, 1.

Yes

No
16.
Describe how the graph of y= x2 can be transformed to the graph of the given equation. (1 point)
y = x2 - 14

Shift the graph of y = x2 right 14 units.

Shift the graph of y = x2 up 14 units.

Shift the graph of y = x2 left 14 units.

Shift the graph of y = x2 down 14 units.
17.
Describe how the graph of y= x2 can be transformed to the graph of the given equation. (1 point)
y = (x-14)2 - 9

Shift the graph of y = x2 down 14 units and then left 9 units.

Shift the graph of y = x2 right 14 units and then up 9 units.

Shift the graph of y = x2 right 14 units and then down 9 units.

Shift the graph of y = x2 left 14 units and then down 9 units.
18.
Describe how to transform the graph of f into the graph of g. (1 point)
f(x) = x4 and g(x) = -x4

Reflect the graph of f across the x-axis.

Shift the graph of f down 1 unit.

Reflect the graph of f across the x-axis and then reflect across the y-axis.

Reflect the graph of f across the y-axis.
19.
The transformation from f to g represents a
stretch. (1 point)
f(x) = Square root of x. and g(x) = 6 Square root of x.

Note: Use all lowercase letters in your response.

20.
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.(1 point)
f(x) = x3 + 4 and g(x) = Cube root of quantity x minus four.

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