Question

(Look at screenshot)

7. The graph represents the height of a passenger car on a ferris wheel, in feet, as a
function of time, in seconds.
Use the graph to help you:

a. Find H(0).
b. Does H(t)=0 have a solution? Explain how you know.
c. Describe the domain of the function.
d. Describe the range of the function.

Answer 1

a. 5 ft

b. No - see below

c. [0, ∞)

d. [5, 55]

Explanation:

From inspection of the graph:

• x-axis: t = time (in seconds)
• y-axis: H(t) = height (in feet)

Part a

When H(0), t = 0 ⇒ y-intercept.

Therefore, from inspection of the graph, H(0) = 5 ft

Part b

H(t) = 0 does not have a solution as the curve never touches the y-axis (when y = 0).

Part c

Domain: set of all possible input values (x-values)

The domain is time (t) (x-axis), therefore the domain is [0, ∞)

Part d

Range: set of all possible output values (y-values)

From inspection of the graph, the lowest value of H(t) is 5 and the highest value of H(t) is 55. Therefore, the range is [5, 55]

Answer 2

Explanation:

Use the graph to dtermine the answer for each part of question

a)

• H(0) = 5

b)

• H(t) = 0 has no solution as its minimum value is 5 feet

c)

• The domain all positive rational numbers, since time is zero or positive.

d)

• The range changes between 5 and 55 feet, according to the graph.