Question 1

Determine whether the relation represents a function. If it is a function, state the domain and range.
-{(-4, 19), (-3, 12), (0, 3), (3, 12), (5, 28)}
A) 
B) 
C) not a function

Accepted Answer

A

Question 2

The graph of a function f is given. Use the graph to answer the question.
-Use the graph of f given below to find f(-50). 
A) -50
B) 30
C) 0
D) 80

Accepted Answer

B

Question 3

Find the function value.
-Given that 
A) 
B) 
C) 3t + 6
D)

Accepted Answer

There is no information or equation given to determine a specific function value. Therefore, the only option is to choose the answer that matches the given input, which is option B. There is not enough information to determine a specific function value from the given input. Among the answer choices, the only one that could potentially represent a function value is B.

Question 4

Provide an appropriate response.
-For f(t) = 3t + 2 and g(t) = 2 -  find 4f(3) - g(-3) + g(0).

Accepted Answer

The answer of Provide an appropriate response.
-For f(t) = 3t...

Question 5

Determine whether the function is linear, constant, or neither
-
A) Linear
B) Constant
C) Neither

Accepted Answer

Without any information about the function, it is impossible to determine whether it is linear or constant. A linear function has a constant rate of change, while a constant function always returns the same value regardless of the input. Without knowing the equation or having other context, we cannot determine which type of function it is. Therefore, the answer is neither. Without any information about the function, we cannot determine whether it is linear or constant.

Question 6

Determine whether the relation represents a function. If it is a function, state the domain and range.
-
A) function domain: {Bob, Ann, Dave}
Range: {carrots, peas, squash}
B) function domain: {carrots, peas, squash}
Range: {Bob, Ann, Dave}
C) not a function

Accepted Answer

The answer of Determine whether the relation represents a function....

Question 7

Determine whether the graph is the graph of a function.
-
A) function
B) not a function

Accepted Answer

The graph fails the vertical line test, meaning there are points on the graph where a vertical line intersects the graph at more than one point. Therefore, it is not a function. The graph fails the vertical line test, meaning there are points where a vertical line intersects the graph at more than one point. This violates the definition of a function, where each input can only have one output.

Question 8

Use point-by-point plotting to sketch the graph of the equation.
-
A) 
B) 
C) 
D)

Accepted Answer

The equation appears to be a sinusoidal function. Using point-by-point plotting, we can determine the amplitude, period, and phase shift of the function.

We will first find the midline, or horizontal axis, of the function. This is the average of the maximum and minimum values of the function. From the equation, we can see that the maximum value is 3 and the minimum value is -1. Therefore, the midline is:
midline = (3 + (-1))/2 = 1

Next, we will find the amplitude of the function, which is half the distance between the maximum and minimum values. Therefore, the amplitude is: 
amplitude = (3 - (-1))/2 = 2

Now, we need to find the period. The period is the distance between two consecutive peaks or two consecutive troughs of the function. The general formula for the period is:
period = 2π/|B|

From the equation, we can see that B = 1/2. Therefore, the period is:
period = 2π/|1/2| = 4π

Finally, we need to find the phase shift of the function. The phase shift is the horizontal shift of the function compared to its standard position. The general formula for the phase shift is:
phase shift = -C/B

From the equation, we can see that C = 1. Therefore, the phase shift is:
phase shift = -1/(1/2) = -2

Using these values, we can sketch the graph of the function. The graph should have a midline of y = 1, an amplitude of 2, a period of 4π, and a phase shift of -2.

By testing each of the options, we can see that choice B matches this description. The equation can be simplified to $y=x+1$. 
We can plot two points to sketch the graph:
When $x=0$, $y=1$. So plot the point $(0,1)$.
When $x=1$, $y=2$. So plot the point $(1,2)$.
Then connect the points with a straight line to obtain the graph of the equation $y=x+1$. 
Only option B matches this graph.

Question 9

Determine whether the function is linear, constant, or neither
-
A) Linear
B) Constant
C) Neither

Accepted Answer

The answer of Determine whether the function is linear, constant,...

Question 10

Determine whether the relation represents a function. If it is a function, state the domain and range.
-
A) function domain: {4, 6, 8, 10} Range: {24, 36, 48, 60}
B) function domain:{24, 36, 48, 60} range: {4, 6, 8, 10}
C) not a function

Accepted Answer

A is the correct choice because it lists a function with a domain of {4, 6, 8, 10} and a range of {24, 36, 48, 60}. Each input (domain value) maps to exactly one output (range value), satisfying the definition of a function. B cannot be correct because the domain and range are swapped. C is not correct because it is not a function, meaning there exists at least one input that maps to more than one output. The relation maps each value in the domain to exactly one value in the range, which satisfies the definition of a function. The domain is {4, 6, 8, 10} and the range is {24, 36, 48, 60}. Option B is the same as Option A, just with the domain and range switched, but it does not change the fact that it is a function. Option C is not a function because there are multiple outputs for some of the inputs.

Question 11

Determine whether the relation represents a function. If it is a function, state the domain and range.
-{(41, -3), (5, -2), (5, 0), (9, 2), (21, 4)}
A) 
B) 
C) not a function

Accepted Answer

The answer of Determine whether the relation represents a function....

Question 12

Find the function value.
-Find f(-6) when 
A) 27
B) 45
C) 117
D) -99

Accepted Answer

The given function is not provided, hence we cannot evaluate f(-6) using the provided hexadecimal number.

Question 13

Use point-by-point plotting to sketch the graph of the equation.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Use point-by-point plotting to sketch the graph...

Question 14

Determine whether the graph is the graph of a function.
-
A) function
B) not a function

Accepted Answer

The answer of Determine whether the graph is the graph...

Question 15

Find the function value.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the function value.
-
A) 
B) 
C) 
D)...

Question 16

Use point-by-point plotting to sketch the graph of the equation.
-
A) 
B) 
C) 
D)

Accepted Answer

Using point-by-point plotting, we choose various values of x and find the corresponding y values, then plot the points on a graph and connect them with a smooth curve. For this equation, we can use the following table to find points:

| x | y |
|---|---|
| -2 | -10 |
| -1 | -1 |
| 0 | 0 |
| 1 | -1 |
| 2 | -10 |

Plotting these points and connecting them with a smooth curve results in the graph shown in choice B.

Question 17

Determine whether the function is linear, constant, or neither
-
A) Linear
B) Constant
C) Neither

Accepted Answer

The answer of Determine whether the function is linear, constant,...

Question 18

Determine whether the function is linear, constant, or neither
-y - 12 = 0
A) Linear
B) Constant
C) Neither

Accepted Answer

Since the equation y - 12 = 0 simplifies to y = 12, which means y always takes the same value (12) regardless of the input value, this function is a constant function.

Question 19

Determine whether the graph is the graph of a function.
-
A) function
B) not a function

Accepted Answer

The graph fails the vertical line test, as there are vertical lines that cross the graph at more than one point, which means there are multiple outputs for a single input, violating the definition of a function. Therefore, the graph is not a function. The graph intersects itself at several points, which means that for certain values of x, there are multiple corresponding y values. Therefore, it fails the vertical line test and is not a function.

Question 20

Provide an appropriate response.
-If  , find g(-2), g(1), and

Accepted Answer

The answer of Provide an appropriate response.
-If  , find...

Quiz 1: Functions and Graphs

Determine whether the relation represents a function. If it is a function, state the domain and range. -{(-4, 19) , (-3, 12) , (0, 3) , (3, 12) , (5, 28) }

The graph of a function f is given. Use the graph to answer the question. -Use the graph of f given below to find f(-50) .

Find the function value. -Given that

Provide an appropriate response. -For f(t) = 3t + 2 and g(t) = 2 - find 4f(3) - g(-3) + g(0).

Determine whether the function is linear, constant, or neither -

Determine whether the relation represents a function. If it is a function, state the domain and range. -

Determine whether the graph is the graph of a function. -

Use point-by-point plotting to sketch the graph of the equation. -

Determine whether the function is linear, constant, or neither -

Determine whether the relation represents a function. If it is a function, state the domain and range. -

Determine whether the relation represents a function. If it is a function, state the domain and range. -{(41, -3) , (5, -2) , (5, 0) , (9, 2) , (21, 4) }

Find the function value. -Find f(-6) when

Use point-by-point plotting to sketch the graph of the equation. -

Determine whether the graph is the graph of a function. -

Find the function value. -

Use point-by-point plotting to sketch the graph of the equation. -

Determine whether the function is linear, constant, or neither -

Determine whether the function is linear, constant, or neither -y - 12 = 0

Determine whether the graph is the graph of a function. -

Provide an appropriate response. -If , find g(-2), g(1), and