1.
Determine whether the graph is the graph of a function. (1 point)
A coordinate axis i...
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Mathematics, 03.03.2020 04:20 culturedxnat
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 β₯ 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 β₯ 0
y < 2
y β₯ 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 β₯ 0
All real numbers
x β₯ -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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