MATH TIME: Functions and Operations on Functions

Open Ended

Why do you think understanding the basic concepts of functions is important in mathematics and real life?

Multiple Choice

Which of the following best describes the process shown in the first image?

• Bread is being toasted to become toast using a toaster.

• Toast is being turned back into bread using a toaster.

• Bread is being cut into slices using a knife.

• Toast is being made without any machine.

Multiple Choice

Based on the table in the second image, what is the role of the 'toaster' in the process?

• It is the input.

• It is the machine that transforms the input to output.

• It is the output.

• It is not involved in the process.

Open Ended

Are the input, machine, and output related? If so, how are they linked together?

Fill in the Blank

A function is a correspondence between two sets of elements such that with each element in the first set (___), there corresponds only one element in the second set (range).

Multiple Select

Select all the correct statements about the definition of a function.

• A function associates each element in the domain with only one element in the range.

• A function can have two outputs for one input.

• Two inputs can have the same output in a function.

• A function does not need a range.

Multiple Choice

Which of the following statements about functions is correct?

• Each element in the domain is associated with only one element in the range.

• Each element in the range is associated with only one element in the domain.

• A function can have multiple outputs for a single input.

• A function does not require a domain.

Multiple Choice

In the mapping shown in the first image, which seat is assigned to Joyce?

• Seat #2

• Seat #3

• Seat #4

• Seat #5

Multiple Choice

Which of the following best describes the concept illustrated by the mapping of names to seat numbers and dates to temperatures in the first two images?

• Function as a mapping from one set to another

• Addition of numbers

• Multiplication of numbers

• Sorting of data

Multiple Choice

Which of the following ordered pairs from the third image does NOT appear in both sets shown?

• (2,4)

• (1,4)

• (2,3)

• (3,2)

Fill in the Blank

In the equation y = 20x, the variable x represents the ___ variable.

Multiple Choice

The height of a tree is related to its age by the equation y = 20x. If the tree is 4 years old, what is its height?

• 80 cm

• 60 cm

• 40 cm

• 100 cm

Fill in the Blank

Fill in the blank: The equation y = ___ + 2x is a function because for every value of x, there is a unique value of y.

^

Open Ended

Explain why the equation x² + y² = 16 does not define y as a function of x.

Multiple Choice

Which of the following equations does NOT represent a function?

• y = x² + 2x

• 10y = x³

• x² + y² = 16

• y = 2x + 5

Multiple Choice

According to the vertical line test, how can you determine if a graph represents a function?

• If every vertical line passes through at most one point on the graph

• If every horizontal line passes through at most one point on the graph

• If the graph is symmetric about the y-axis

• If the graph has no intercepts

Multiple Choice

What are the four representations of functions mentioned in the lesson introduction?

• Sets (mapping), Sets (ordered pairs), Equation, Graph

• Equation, Table, Graph, Mapping

• Graph, Table, List, Equation

• Ordered pairs, Table, Mapping, List

Multiple Select

Which of the following are steps involved in evaluating a function?

• Substitute the given value for the variable

• Simplify the resulting expression

• Draw the graph of the function

• Find the inverse of the function

Fill in the Blank

Evaluate g(x) = 3x² - 4 when x = -2. The answer is ___.

Multiple Choice

What is the value of f(x) = 2x + 1 when x = 3?

• 7

• 5

• 6

• 9

Multiple Choice

Which of the following best describes the process of evaluating a function?

• Replacing the variable with a given number or expression

• Drawing the graph of the function

• Finding the domain of the function

• Solving for x in the equation

Multiple Choice

Which of the following best describes a mathematical function?

• A relationship where each input has exactly one output

• A set of random numbers

• A process with multiple possible outputs for each input

• A list of unrelated values

Multiple Choice

If f(x)= 9x²+2x-3, find f(-1).

• -4

• 14

• -14

• 4

Multiple Choice

Evaluate f(x)= 2x² + 5x - 17 for f(-1)

• -20

• -10

• -24

• -14

Multiple Choice

If f(x) = 2x + 5, find f(-3).

• 1

• -1

• 4

• -4

Multiple Choice

If $$f\left(x\right)\ =\ x-1$$ and $$g\left(x\right)=5x-2$$ , then  $$\left(f+g\right)\left(x\right)=$$

• $$5x^2+1$$  

• $$5x^2-3$$  

• $$6x+1$$  

• $$6x-3$$  

Multiple Choice

If $$f\left(x\right)\ =\ x-1$$ and $$g\left(x\right)=5x-2$$ , then  $$\left(f-g\right)\left(x\right)=$$

• -4x - 3

• -4x +1

• 6x + 1

• 6x - 3

Multiple Choice

If $$f\left(x\right)\ =\ x-1$$ and $$g\left(x\right)=5x-2$$ , then  $$\left(f\cdot g\right)\left(x\right)=$$

• $$5x-3$$  

• $$5x^2+2$$  

• $$5x^2-7x+2$$  

• $$5x-7$$  

Multiple Choice

If $$f\left(x\right)\ =\ x-1$$ and $$g\left(x\right)=5x-2$$ , then  $$\left(\frac{f}{g}\right)\left(x\right)$$

• $$\frac{x-1}{5x-2}$$  

• $$\frac{5x-2}{x-1}$$  

• $$\frac{-1}{3}$$  

• $$-3$$  

Multiple Choice

If $$f\left(x\right)\ =\ 3x^2-4$$ and $$g\left(x\right)=x^2-8x+4$$ , then  $$\left(f+g\right)\left(x\right)=$$

• $$4x^4-8x-8$$  

• $$4x^4-8x$$  

• $$4x^2-8x-8$$  

• $$4x^2-8x$$  

Multiple Choice

If $$f\left(x\right)\ =\ 3x^2-4$$ and $$g\left(x\right)=x^2-8x+4$$ , then  $$\left(f-g\right)\left(x\right)=$$

• $$2x^2-8x-8$$  

• $$2x^2+8x-8$$  

• $$2x^2-8x$$  

• $$2x^2+8x$$  

Multiple Choice

If $$f\left(x\right)\ =\ 3x^2-4$$ and $$g\left(x\right)=x^2-8x+4$$ , then  $$\left(f\cdot g\right)\left(x\right)=$$

• $$3x^4-24x^3+8x^2+32x-16$$  

• $$3x^4-8x-16$$  

• $$3x^4-24x^3+8x^2-32x-16$$  

• $$3x^4-24x^3+16x^2+32x-16$$  

Multiple Choice

If $$f\left(x\right)\ =\ 3x^2-4$$ and $$g\left(x\right)=x^2-8x+4$$ , then  $$\left(\frac{f}{g}\right)\left(x\right)=$$

• $$\frac{3x^2-4}{x^2-8x+4}$$  

• $$\frac{x^2-8x+4}{3x^2-4}$$  

• $$\frac{3x^2-1}{x^2-8x}$$  

• $$\frac{1}{-4x}$$  

Open Ended

What is one key concept you learned about functions in today's lesson?