8th grade · Math · Unit 14 of 17
Functions
One input, one output
What your child practices
Deciding whether a relation is a function, comparing two functions shown in different ways, spotting linear functions, and matching a graph to a story.
Alaska content standards learning standard: 8.F.1; 8.F.2; 8.F.3; 8.F.5 · functions as one output for each input, comparing functions, linear functions, and describing graphs in words
How we explain it
Children can open this short lesson before they practice.
- A function gives each input exactly one output.
- A repeated x with two different y-values is not a function.
- A linear function has a constant rate of change: y = mx + b.
Example: Is {(1, 4), (2, 5), (1, 6)} a function? The input 1 has two outputs, 4 and 6. Answer: No
Functions in Alaska
In the Alaska content standards, this is unit 14 of 17 in 8th grade Math, after Systems of Equations and before Cones, Cylinders & Spheres.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Source: Alaska Department of Education and Early Development
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
Which equation is NOT a linear function?
- y = x
- y = x²
- y = 0.5x + 4
- y = −2x + 5
y = x²
Hint: A linear function has the form y = mx + b. Look for x squared, cubed, in an exponent or in the denominator.
Question 2
Is this relation a function?
x y 2 4 7 -1 5 4 1 6 - No, one input has two different outputs
- Yes, each input has exactly one output
Yes, each input has exactly one output
Hint: A function gives each input (x) exactly one output (y). Look for a repeated x with different y-values.
Question 3
The graph is a straight line going up from the origin. Which situation fits best?
- A ball thrown up and coming down
- A phone battery that is charging and then unplugged
- The height of a swing over time
- Total cost of apples at a fixed price per pound
Total cost of apples at a fixed price per pound
Hint: Read the graph left to right: going up means increasing, flat means not changing, going down means decreasing.
Question 4
Function A is y = 7x + 3. Function B is shown in the table. Which has the greater rate of change?
Function B x y 0 5 1 10 2 15 - Function A
- Function B
- They are the same
Function A
Hint: A's rate is 7. B's rate is how much y goes up each time x goes up 1.
Question 5
The rule is y = −x + 9. What is the output when the input is −3?
answer box
12
Hint: Replace x with −3: −1 × (−3) + 9.
Question 6
The rule is y = −3x + 1. What is the output when the input is −3?
answer box
10
Hint: Replace x with −3: −3 × (−3) + 1.