Functions & Domain
A vending machine gives one snack for each button pressed. Is this relationship a function?
Yes. Each input has exactly one output.
Identify the slope in y = 7x + 4.
7
Which equation is proportional: y = 4x or y = 4x + 2?
y=4x
Plan A costs $10 monthly. Plan B costs $15 monthly. Which has the greater rate of change?
Plan B
A line rises from left to right. Is its slope positive or negative?
Positive
Find the domain: {(1, 5), (2, 8), (3, 11)}.
{1, 2, 3}
A taxi charges $5 to start and $3 per mile. What is the y-intercept?
$5
A babysitter earns $12 per hour with no starting fee. Write the equation.
y=12x
Function A: y = 3x + 5. Function B: y = 3x + 9. Which has the greater initial value?
Function B
A plant is 6 cm tall and grows 2 cm each week. What does the 6 represent?
Initial Height
Is {(2, 4), (3, 6), (2, 8)} a function? Explain.
No. Input 2 has two different outputs.
Find the slope from (1, 6) and (3, 14).
4
Rewrite 3x + y = 15 in slope-intercept form.
y = −3x + 15
A table shows (0,2), (1,7), (2,12). Compare its slope with y = 4x + 6.
Table slope 5 is greater than 4.
A pool starts with 120 gallons and drains 8 gallons per minute. Write an equation.
y=120-8x
A student buys whole-number quantities of movie tickets, including zero. What values belong to the domain?
Nonnegative integers: 0, 1, 2, 3, ...
A table has points (0,18), (1,13), (2,8), (3,3). Find the slope and y-intercept.
Slope = −5; y-intercept = 18.
A parking garage costs $6 initially and $4 per hour. Write the equation.
y=4x+6
Gym A charges $20 to join and $15/month. Gym B charges $35 to join and $10/month. Which is cheaper after 4 months?
Gym B: $75; Gym A: $80.
A lake depth decreases, increases after rain, then decreases more slowly. Describe its graph.
Downward, upward, then downward less steeply.
A water tank contains 80 gallons and loses 5 gallons each minute. What is the realistic domain until empty?
0 ≤ x ≤ 16 minutes.
A phone battery drops from 90% at 0 hours to 30% in 4 hours at a constant rate. What is the slope and its meaning?
−15 percentage points per hour.
Rewrite y − 20 = −3(x − 4) in slope-intercept form. Identify the initial value.
y = −3x + 32; initial value = 32.
Find the slope of the line that includes the following points. (-12, -9) (-3, -3)
-6/-9 = 6/9 = 2/3
A machine starts with 100 oz and uses 5 oz/min. Another uses 3 oz/min for the same 20 minutes. How does the graph change?
Slope changes from −5 to −3; initial value can stay 100.