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.
Washington State Learning Standards learning standard: M.8.R.F.1; M.8.R.F.2; M.8.R.F.3; M.8.R.F.5 · understanding functions as rules with exactly one output for each input, comparing functions, recognizing linear functions, and describing graphs qualitatively
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
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
The graph rises steadily, then stays flat, then falls back to zero. Which situation fits best?
- A plant that grows faster and faster
- A bath filling up and never draining
- A bike ride away from home, a rest, then the ride back home
- A car that never stops moving
A bike ride away from home, a rest, then the ride back home
Hint: Read the graph left to right: going up means increasing, flat means not changing, going down means decreasing.
Question 2
Function A is y = 4x. 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 B
Hint: A's rate is 4. B's rate is how much y goes up each time x goes up 1.
Question 3
Is this relation a function?
x y 1 -1 2 -2 3 9 5 6 - Yes, each input has exactly one output
- No, one input has two different outputs
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 4
Which equation is a linear function?
- y = 7 − x
- y = 1/x
- y = x²
- y = x² − 3
y = 7 − x
Hint: A linear function has the form y = mx + b: x is not squared, cubed, an exponent or under a fraction bar.
Question 5
The rule is y = x + 4. What is the output when the input is −2?
answer box
2
Hint: Replace x with −2: 1 × (−2) + 4.
Question 6
The rule is y = x + 5. What is the output when the input is 2?
answer box
7
Hint: Replace x with 2: 1 × 2 + 5.