Review of functions (Lesson Quiz)

Review;
Functions & Graph Behaviour

By William Katumba

Functions; The heart of Pre-Calculus

A function is a mathematical relationship that maps a set of input values to a set of output values. In the figure to the right, we see a function machine.

To write that y is a function of x, we call the function f and say that
y = f(x)

Multiple Choice

Which of the following is the correct notation of a function for this situation?

"The time to fill a bathtub is a function of the rate that water comes from the faucet."

• r = f(t)

• t = r(f)

• t = f(x)

• t = f(r)

Multiple Choice

Which of the following is the correct notation of a function for this situation?

"The cost of an iPhone is a function of how much memory it has."

• c = f(m)

• m=f(c)

• C = f(x)

• M=f(x)

Open Ended

Generate a function, describing this situation;

"The number of points (P) blood pressure falls is a function of the amount of a medication (m) taken"

Open Ended

Generate a function, describing this situation;

"The temperature (T) of a broiler is a function of the amount of time (t) it is heated."

Domain and Range:

In a function, the set of allowable input values is called the domain of the function. The set of allowable output values is called the range of the function.

Dropdown

Consider the function description;

"The cost of an Iphone is a function of how much memory it has."

The domain is ​

Select answer

and the range is ​

Select answer

Dropdown

Consider the function description;

"The time to fill a bathtub is a function of the rate that water comes from the faucet."

The domain is ​

Select answer

and the range is ​​

Select answer

Dropdown

Consider the function description;

"The temperature of a broiler is a function of the amount of time it is heated."

The domain is ​

Select answer

and the range is ​​

Select answer

Multiple Choice

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

• D: {1, -3, -4,}
  R: {0, 1, 2, -4}
• D:{0, 1, 2, -4}
  R:{1, -3, -4}
• D:{0, 1, 2, 3, 4}
  R:{1, -3, -4}

Multiple Choice

What is the domain?

• x≥0

• y≥0

• All real numbers

• {0, 1, 2, 3, 4,...}

Multiple Choice

What is the range?

• x≥0

• y≥0

• All real numbers

• {0, 1, 2, 3, 4,...}

Multiple Choice

What is the DOMAIN?

• {1, 2, 3, 4}

• {-3, 0, 3}

• {-3, 1, 2, 5}

• {1, 2, -3, 5}

Multiple Choice

In the given relation, what domain value corresponds to the range value -2?

{(-1, 2), (-2, 4), (2, 5), (0, -2), (2, 0)}

• -2

• 2

• 4

• 0

Multiple Choice

What is the domain of this relation?

• -2, 0, 2 and 4

• -8, 0, 8 and 16

• -2, 0 and 2

• x and y

Function Definition:

In a function, for every x in the domain, there can only be one and only one y in the range. What this says is that no x-value can repeat. However, it is possible for a y-value to repeat.

Multiple Choice

Does this mapping represent a function?

• Maybe
• No
• Not enough information
• Yes

Multiple Choice

Does this mapping represent a function?

• Maybe
• No
• Not enough information
• Yes

Multiple Choice

Does this mapping represent a function?

• Maybe
• No
• Not enough information
• Yes

Multiple Choice

Does this mapping represent a function?

• Maybe
• No
• Not enough information
• Yes

Determining if a graph represents a function;

Vertical Line Test

If a vertical line drawn anywhere on the graph intersects more than once, it cannot be a function​

Multiple Choice

Which table represents a linear function?

• Table A

• Table B

Multiple Choice

.

• Function
• Not a Function

Multiple Choice

DOES THIS GRAPH REPRESENT A FUNCTION?

• NO

• YES

Multiple Choice

Which graph does NOT pass the vertical line test?

• Graph 1
• Graph 2
• Graph 3
• Graph 4

Multiple Choice

Is this graph a function or not a function? 

• Function 
• Not a Function 

Multiple Choice

Is this graph a function or not a function? 

• Function
• Not a Function

Multiple Choice

Is this table a function or not a function? 

• Function
• Not a Function

Multiple Choice

Is this a function or not a function?

• Function
• Not a Function

Multiple Choice

Which set of ordered pairs is a function?

• {(9,5), (10,5), (9,-5), (10,-5)}

• {(3,4), (4,-3), (7,4), (3, 8)}

• {(6,-5), (7, -3), (8, -1), (9, 1)}

• {(2, -2), (5, 9), (5, -7), (1, 4)}

Multiple Choice

Is the relation a function? Why.

• Yes, because the x-value 11 has two y-values pair with it.
• Yes, because each x-value has only one y-value paired with it.
• No, because the x-value 11 has two y-values pair with it.
• No, because each x-value has only one y-value paired with it.

What is interval notation?

• System that helps communicate sets (regions) of numbers

• A short alternative to using inequalities like <, >, ≤ , ≥

• Uses brackets for included values (closed circle) and parenthesis for non-included values (open circle).

Multiple Choice

Look at the Graph. Write the inequality in interval notation.

• [-4, -1)

• (-4, -1)

• (-4, -1]

• [-4, -1]

Multiple Choice

Express the following in Interval Notation

-9 < x ≤ -4

• [-9, -4]

• (-9,-4]

• [-9, -4]

• (-9,-4)

Multiple Choice

Look at the picture. Which number line corresponds to [-2, 5]?

• Graph 1

• Graph 2

• Graph 3

• Graph 4

Multiple Choice

Express the following in Interval Notation

-8 ≤ x < 8

• [-8, 8]

• [-8,8)

• (-8, 8]

• (-8, 8)

Multiple Choice

Write the inequality in interval notation. x > -1

• (-∞, -1)

• (-1, ∞]

• (-∞, -1]

• (-1, ∞)

Multiple Choice

What interval notation does the number line graph represent?

• [∞, -5)

• (∞, -5)

• [-5, ∞)

• (-5, ∞)

Multiple Choice

Write the following in interval notation

x ≥ 100

• (0, 100] (Real quick)

• (∞, 100]

• [100, ∞)

• (∞, 100)

Multiple Choice

Write the following solution in interval notation:

z < 20

• ( -∞ , 20 )

• ( 20,∞)

• ( -∞ , 20)

• ( -∞ , 20]

Multiple Choice

Write the following in interval notation

x < 8

• (8, ∞)

• (8, -∞)

• (-∞, 8)

• [-∞, 8]

Increasing, Decreasing, Positive, and Negative Intervals

How do I find where a graph is increasing, decreasing, positive, or negative?

Multiple Choice

Is the function positive or negative from a to b?

• Positive

• Negative

Multiple Choice

Is the function positive or negative from c to d?

• Positive

• Negative

Multiple Choice

Is the function positive or negative from $$-\infty$$ to a?

• Positive

• Negative

Multiple Choice

Is the function positive or negative from b to c?

• Positive

• Negative

Multiple Choice

Is the function increasing or decreasing on the interval

from e to ∞? 

• Increasing

• Decreasing

Multiple Choice

Where is the function decreasing?

• x<1

• x>1

• x<2

• x>2

Multiple Choice

Identify where the function is decreasing.

• x < -4 , x > 1

• -4 < x < 1

• -6 < x < 7.5

• All Real Numbers

Multiple Choice

Identify where the function is increasing.

• x < -5 , x > 8

• -1 < x < 8

• -5 < x < -1 , x > 8

• x < -5 , -1 < x < 8

Multiple Choice

Which open interval is the function increasing?

• $$\left(-\infty,0\right)$$  

• $$\left(0,2\right)$$  

• $$\left(2,\infty\right)$$  

Multiple Choice

Which open interval is the function decreasing?

• $$\left(-\infty,0\right)$$  

• $$\left(0,2\right)$$  

• $$\left(2,\infty\right)$$  

Multiple Choice

Which open interval is the function constant?

• $$\left(-\infty,0\right)$$  

• $$\left(0,2\right)$$  

• $$\left(2,\infty\right)$$  

Multiple Select

Which interval is the function decreasing on?

Select all that apply.

• $$\left(-\infty,\infty\right)$$  

• $$\left(-\infty,-1\right)$$  

• $$\left(1,\infty\right)$$  

• $$\left(-1,1\right)$$  

Multiple Select

Which interval is the function increasing on?

Select all that apply.

• $$\left(-\infty,\infty\right)$$  

• $$\left(-\infty,-1\right)$$  

• $$\left(1,\infty\right)$$  

• $$\left(-1,1\right)$$  

Concavity; 'The curvature of a graph'

Concave down

• f looks 'U' shaped

• The rate of change is increasing

Concave down

• f looks 'n' shaped

• The rate of change is decreasing

Multiple Choice

Over what intervals will the second derivative of f(x) be negative?

• $$\left(-\infty,-1\right)$$
  

• $$\left(-\infty,1\right)$$

• $$\left(1,\infty\right)$$

• $$\left(-1,1\right)$$

Multiple Select

Find the point(s) of inflection (if it exists) of the graphed function.

• No point of inflection

• Points 3 and 5

• Points 1, 3, 5 and 7

• Points 1, 2, 3, 4, 5, 6 and 7

• Points 2, 4 and 6

Multiple Select

Find the point(s) of inflection (if it exists) of the graphed function.

• No point of inflection

• Points K, R, and S.

• Points K and S

• Points P, Q, K, R, S, and T

Multiple Select

Find the point(s) of inflection (if it exists) of the graphed function. 

• No point of inflection 

• Points A and B

• Points  A, B and Z

• Points X, A, Y, B, Z

Extra Practice

Multiple Choice

What is the domain?

• $$\left(-\infty,\ -3\right]$$
  

• $$\left[3,\ -\infty\right)$$
  

• $$\left(-\infty,3\right]$$

• $$\left(-\infty,\infty\right)$$

• None of the answer choices

Multiple Choice

What is the range?

• $$\left(-\infty,\ -3\right]$$
  

• $$\left[3,\ -\infty\right)$$
  

• $$\left(-\infty,3\right]$$

• None of the answer choices

• $$\left[-3,\ \infty\right)$$  

Multiple Choice

What is the range of the graph?

• (-∞,∞)
• [-1,0]
• [-1,3]
• [3,∞)

Multiple Choice

What is the domain?

• (-3 , 3)
• [-4, 5]
• (-4, 5)
• (-3, 3]

Multiple Choice

What is/are the increasing interval(s) for the function shown?

• $$\left(-3,\ 1\right)$$

• $$\left(4,\ 8\right)$$

• $$\left(-\infty,1\right)\ and\ \left(-3,\ 1\right)$$

Multiple Choice

What is the increasing interval on the function shown?

• $$\left(-\infty,\ 1\right)$$

• $$\left(-\infty,\ 2\right)$$

• $$\left(2,\ \infty\right)$$

• $$\left(1,\ \infty\right)$$

Multiple Choice

What is the decreasing interval on the function shown?

• $$\left(-\infty,\ -3\right)$$

• $$\left(-\infty,\ -4\right)$$

• $$\left(-4,\ \infty\right)$$

• $$\left(-3,\ \infty\right)$$

Multiple Choice

At which following point does the graph of f(x) appear to be transitioning from concave down to concave up?

• B

• E

• G

• H

Multiple Choice

Over which interval is the graph of f(x) both decreasing and concave up?

• (B, C)

• (D, E)

• (C, D)

• (H, I)

Multiple Choice

Determine the concavity of this graph.

• Concave Up

• Concave Down

• Neither (Linear)

Multiple Choice

Determine the concavity of this graph.

• Concave up

• Concave down

• Neither (linear)