Question

1. going to the trampoline park is modeled by f(h) = $14.50h + $16. evaluate the function for f(6) and interpret its meaning.

work:
interpret:

1. determine whether each situation is discrete (counted data) or continuous (measured data).

i buy x books for $5.95 each.
you eat x whole granola bars at 95 calories each.
you eat granola bars at 95 calories.
the amount it rains per month.
discrete or continuous
discrete or continuous
discrete or continuous
discrete or continuous

1. select all non - linear functions.

□ y = 3x³+2
□ 5 = - 2x + y
□ x + 3y = 25
□ y = 3^x
□ y = x² - x - 12
□ - 4x = 3y - 2

1. determine whether the function is discrete, continuous or neither. put an x in the correct box

function
discrete
continuous
neither

Explanation:

Step1: Evaluate f(6) for f(h)=14.5h + 16

Substitute h = 6 into the function: f(6)=14.5×6 + 16

Step2: Calculate the product

14.5×6 = 87, so f(6)=87 + 16

Step3: Calculate the sum

87+16 = 103

Interpretation: The cost of going to the trampoline park for 6 hours is $103.

Step4: Determine data - type for "I buy x books for $5.95 each"

The number of books x is counted, so it is discrete data.

Step5: Determine data - type for "You eat x whole granola bars at 95 calories each"

The number of whole granola bars x is counted, so it is discrete data.

Step6: Determine data - type for "You eat granola bars at 95 calories"

The amount of granola bars eaten can be a fraction or decimal, so it is continuous data.

Step7: Determine data - type for "The amount it rains per month"

The amount of rain is measured and can be a fraction or decimal, so it is continuous data.

Step8: Identify non - linear functions

A linear function has the form y=mx + b.
For y = 3x³+2, the highest power of x is 3, so it is non - linear.
For 5=-2x + y (or y = 2x+5), it is linear.
For x + 3y = 25 (or y=-\frac{1}{3}x+\frac{25}{3}), it is linear.
For y = 3^x, it is an exponential function and non - linear.
For y=x² - x - 12, the highest power of x is 2, so it is non - linear.
For - 4x = 3y - 2 (or y=-\frac{4}{3}x+\frac{2}{3}), it is linear.

Step9: Determine function type for graphs

A discrete function has distinct, separate points. A continuous function has a smooth, unbroken curve.
(Without seeing the actual graphs, assume we know the rules): If the graph has distinct points, it is discrete. If it is a smooth curve, it is continuous.

Answer:

f(6)=103. The cost of going to the trampoline park for 6 hours is $103.
I buy x books for $5.95 each: Discrete
You eat x whole granola bars at 95 calories each: Discrete
You eat granola bars at 95 calories: Continuous
The amount it rains per month: Continuous
Non - linear functions: y = 3x³+2, y = 3^x, y=x² - x - 12
(Graph - related answers depend on actual visual inspection of graphs)