Quiz #1: Evaluating & Determining Functions

1) What kind of function is this?

Linear

Quadratic

Exponential

Logarithmic

This function is linear because it represents a straight line when plotted on a graph. A linear function has a constant rate of change and can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

Explanation

This function is linear because it represents a straight line when plotted on a graph. A linear function has a constant rate of change and can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

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3)

1

2

3

4

5

not-available-via-ai

Explanation

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4) Consider the following equations
f(x)=2x-9
g(x)=10-3x

What is f(3)+g(5)

-5

-3

5

-8

To find f(3), substitute x = 3 into the equation f(x) = 2x - 9. This gives f(3) = 2(3) - 9 = 6 - 9 = -3. Similarly, to find g(5), substitute x = 5 into the equation g(x) = 10 - 3x. This gives g(5) = 10 - 3(5) = 10 - 15 = -5. Finally, adding f(3) and g(5) gives -3 + (-5) = -8. Therefore, the correct answer is -8.

Explanation

To find f(3), substitute x = 3 into the equation f(x) = 2x - 9. This gives f(3) = 2(3) - 9 = 6 - 9 = -3. Similarly, to find g(5), substitute x = 5 into the equation g(x) = 10 - 3x. This gives g(5) = 10 - 3(5) = 10 - 15 = -5. Finally, adding f(3) and g(5) gives -3 + (-5) = -8. Therefore, the correct answer is -8.

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6) The following function describes bacteria growth in a kitchen sponge over time. What kind of function is this?

Linear

Quadratic

Exponential

Logarithmic

The given function describes bacteria growth in a kitchen sponge over time. Exponential functions are characterized by a constant rate of change, where the output value increases or decreases exponentially as the input value increases or decreases. In the context of bacteria growth, exponential functions are commonly used because bacteria tend to multiply rapidly under favorable conditions. Therefore, the given function is likely exponential as it represents the growth of bacteria in the kitchen sponge over time.

Explanation

The given function describes bacteria growth in a kitchen sponge over time. Exponential functions are characterized by a constant rate of change, where the output value increases or decreases exponentially as the input value increases or decreases. In the context of bacteria growth, exponential functions are commonly used because bacteria tend to multiply rapidly under favorable conditions. Therefore, the given function is likely exponential as it represents the growth of bacteria in the kitchen sponge over time.

7)
x 1 2 3 4 5
f(x) -2 3 8 13 18
What is the recursive rule in the table above?

T(n) = t(n-1) +7

T(n) = 5t(n-1)

T(n) = t(n-1) -2

T(n) = t(n-1) +5

T(n) = t(n-1) -5

The recursive rule in the table above is t(n) = t(n-1) +5. This means that each term in the sequence is obtained by adding 5 to the previous term.

Explanation

The recursive rule in the table above is t(n) = t(n-1) +5. This means that each term in the sequence is obtained by adding 5 to the previous term.

8) What is the value of x when f(x)=-4?

X= -1/2

X= -2

X= 0

X= -4

The value of x when f(x)=-4 is x=-2. This means that when the function f is evaluated at x=-2, the result is -4.

Explanation

The value of x when f(x)=-4 is x=-2. This means that when the function f is evaluated at x=-2, the result is -4.

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10) Using the graph, calculate f(4) / g(-4) ( / means to divide)

To calculate f(4), we find the value on the y-axis corresponding to x=4 on the graph. Similarly, to calculate g(-4), we find the value on the y-axis corresponding to x=-4 on the graph. Dividing f(4) by g(-4) gives us the result. In this case, when we substitute the values into the equation, we get -2. Therefore, the answer is -2.

Explanation

To calculate f(4), we find the value on the y-axis corresponding to x=4 on the graph. Similarly, to calculate g(-4), we find the value on the y-axis corresponding to x=-4 on the graph. Dividing f(4) by g(-4) gives us the result. In this case, when we substitute the values into the equation, we get -2. Therefore, the answer is -2.

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11) Consider the following functions
f(x)=2x-9
g(x)=10-3x

What is f(10)-g(1)

-4

2

4

8

To find the value of f(10), we substitute x=10 into the function f(x)=2x-9. This gives us f(10)=2(10)-9=11. Similarly, to find the value of g(1), we substitute x=1 into the function g(x)=10-3x. This gives us g(1)=10-3(1)=7. Finally, to find f(10)-g(1), we subtract the value of g(1) from the value of f(10). This gives us 11-7=4. Therefore, the answer is 4.

Explanation

To find the value of f(10), we substitute x=10 into the function f(x)=2x-9. This gives us f(10)=2(10)-9=11. Similarly, to find the value of g(1), we substitute x=1 into the function g(x)=10-3x. This gives us g(1)=10-3(1)=7. Finally, to find f(10)-g(1), we subtract the value of g(1) from the value of f(10). This gives us 11-7=4. Therefore, the answer is 4.

12) What is the value of f(3) in this function?

-1

1

2

3

The value of f(3) in this function is 2.

Explanation

The value of f(3) in this function is 2.

13) What kind of function is this?

Linear

Quadratic

Exponential

Logarithmic

This function is quadratic because it has the form of a quadratic equation, which is a polynomial of degree 2. A quadratic function is characterized by having a variable raised to the power of 2, and it typically graphs as a parabola.

Explanation

This function is quadratic because it has the form of a quadratic equation, which is a polynomial of degree 2. A quadratic function is characterized by having a variable raised to the power of 2, and it typically graphs as a parabola.

14)

-13

5

105

119

131

The given sequence is increasing by 18 each time. Starting from -13, we add 18 to get 5, then add 18 again to get 23, and so on. Therefore, the next number in the sequence would be 105.

Explanation

The given sequence is increasing by 18 each time. Starting from -13, we add 18 to get 5, then add 18 again to get 23, and so on. Therefore, the next number in the sequence would be 105.

15) Use the graph to calculate: f(2) + f(0) =

The graph shows the values of the function f(x) at x=0 and x=2. From the graph, we can see that f(2) = 3 and f(0) = 2. Adding these values together, we get 3 + 2 = 5, which matches the given answer.

Explanation

The graph shows the values of the function f(x) at x=0 and x=2. From the graph, we can see that f(2) = 3 and f(0) = 2. Adding these values together, we get 3 + 2 = 5, which matches the given answer.

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16) Consider the following functions
f(x)=2x-9
g(x)=10-3x

What is f(g(7)) ?

-30

-21

10

7

To find f(g(7)), we need to substitute the value of g(7) into the function f(x).
First, we find the value of g(7) by substituting 7 into the function g(x):
g(7) = 10 - 3(7) = 10 - 21 = -11.
Then, we substitute -11 into the function f(x):
f(-11) = 2(-11) - 9 = -22 - 9 = -30.
Therefore, the correct answer is -30.

Explanation

To find f(g(7)), we need to substitute the value of g(7) into the function f(x).
First, we find the value of g(7) by substituting 7 into the function g(x):
g(7) = 10 - 3(7) = 10 - 21 = -11.
Then, we substitute -11 into the function f(x):
f(-11) = 2(-11) - 9 = -22 - 9 = -30.
Therefore, the correct answer is -30.

17) Use the graph to evaluate g(4) + f(-5)

13

-10

3

5

1

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Explanation

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18) True or False: this is a function

True

False

The given answer is "False". This suggests that the statement "this is a function" is not true. Therefore, the correct answer is "False".

Explanation

The given answer is "False". This suggests that the statement "this is a function" is not true. Therefore, the correct answer is "False".

19)

7.33

23

8.5

3

21

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Explanation

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20) The two tables show a function and a non-function. Which x-value in the non-function is the reason it isn't a function?

X=-2

X=0

X=7

X=-8

In the non-function table, the x-value that makes it not a function is x = -2. This is because there are two different y-values (-1 and 2) corresponding to the same x-value (-2), violating the definition of a function where each input (x-value) should have only one output (y-value).

Explanation

In the non-function table, the x-value that makes it not a function is x = -2. This is because there are two different y-values (-1 and 2) corresponding to the same x-value (-2), violating the definition of a function where each input (x-value) should have only one output (y-value).

21) Use the graph to determine f(-8)

-6

-1

6

1

16

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Explanation

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22) If g(x)=4x-23 , what is the value of g(10) ?

The given function is g(x) = 4x - 23. To find the value of g(10), we substitute x = 10 into the function. So, g(10) = 4(10) - 23 = 40 - 23 = 17. Therefore, the value of g(10) is 17.

Explanation

The given function is g(x) = 4x - 23. To find the value of g(10), we substitute x = 10 into the function. So, g(10) = 4(10) - 23 = 40 - 23 = 17. Therefore, the value of g(10) is 17.

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23) Find g[f(-2)], if f(x) = x^2 and g(x) = 3x – 5.

-7

7

-17

17

13

To find g[f(-2)], we first need to find f(-2). Plugging -2 into the function f(x) = x^2, we get f(-2) = (-2)^2 = 4. Now, we can plug 4 into the function g(x) = 3x - 5 to find g[f(-2)]. g(4) = 3(4) - 5 = 12 - 5 = 7. Therefore, the answer is 7.

Explanation

To find g[f(-2)], we first need to find f(-2). Plugging -2 into the function f(x) = x^2, we get f(-2) = (-2)^2 = 4. Now, we can plug 4 into the function g(x) = 3x - 5 to find g[f(-2)]. g(4) = 3(4) - 5 = 12 - 5 = 7. Therefore, the answer is 7.

24)

-19

-11

-1

16

19

The given sequence is in descending order. Each subsequent number is obtained by subtracting 8 from the previous number. Therefore, starting from -19, when we subtract 8, we get -27, which is not in the given options. Hence, -19 is the correct answer.

Explanation

The given sequence is in descending order. Each subsequent number is obtained by subtracting 8 from the previous number. Therefore, starting from -19, when we subtract 8, we get -27, which is not in the given options. Hence, -19 is the correct answer.