Where the function?
What makes a relation a function?
A function has exactly one output (y-value) for each input (x-value).
What is the slope in the equation y = 2x + 3?
2
A cab charges $8 plus $0.75 per mile. What is the equation?
c = 0.75m + 8
What does a horizontal line mean on a graph?
No change; rate is 0
What does the y-intercept usually represent?
The starting value or initial amount.
Is the set {(1, 2), (2, 3), (2, 4)} a function? Why or why not?
No, because the input 2 is paired with two different outputs (3 and 4).
Identify the y-intercept in y = -4x + 10.
10
Ralph gives 10 lollipops every 5 days. Rate per day?
2 lollipops per day
Two x-values have same y-value. Still a function?
Yes, as long as each x is used once.
Natasha earns $12.50/hour post-raise. What does this show?
It's her rate of pay (slope of line).
What is the vertical line test and how does it relate to functions?
If a vertical line touches the graph more than once, it's not a function.
Write the equation of a line with slope 3 and y-intercept -2.
y=3x-2
Tech charges $75 flat + $45/hour. What’s the equation?
y = 45x + 75
In a table, x = 0 gives y = 12. What’s the y-intercept?
12
Trucker drives 100 mi in 2 hours. Average speed?
50 mph
A table shows x-values 0, 1, 2, 3 and y-values 5, 6, 7, 7. Is this a function?
Yes, each x-value maps to only one y-value, even if y-values repeat.
Is y = x² + 2 linear or nonlinear? Explain
Nonlinear, because x is squared
A blizzard adds 24 inches in 6 hours. What’s the rate?
4 inches per hour
What does (4, 140) mean on a distance-time graph?
After 4 hours, traveled 140 miles.
y = 4x + 164. What do slope and intercept mean?
Slope = $4 per degree, y-intercept = $164 at 0°F.
Explain why {(3, 11), (6, 1), (6, 4)} is not a function.
Because x = 6 has two different outputs (1 and 4), violating the function rule.
A graph shows y = 0.5x + 10. What does slope mean in context?
Slope = 0.5, meaning it increases $0.50 per unit of x.
y = 0.5x + 10 for life insurance. What do x, y, and slope mean?
x = age, y = monthly cost, slope = $0.50 per year
Table: x = 0, 0, 1, 2 → y = 10, 8, 7, 6. Is it a function?
No, x = 0 has two outputs.
Company charges $2,000 flat + $3/mile. Slope? Y-int?
Slope = 3, y-intercept = 2000; shows cost increases linearly.