Question

Bungee Jumping Luisa goes bungee jumping from a 500 -ft- high bridge. The graph shows Luisa’s height $h\left(t\right)$(in ft) after t seconds.

1. Describe in words what the graph indicates from about Luisa’s bungee jump.
2. Suppose Luisa goes bungee jumping froma 400 -ft- high bridge. Sketch a new graph that shows Luisa’s height $H\left(t\right)$after t seconds.
3. What transformation must be performed on the function hto obtain the function H? Express the function Hin terms of h.

Short answer

(a) The graph indicates that the Luisa’s bungee jump is decrease in every increase of time.

(b) If Luisa goes jump from a 400 ft- high. The new graph that shows the Luisa’s height H(t) after t seconds are,

(c) We apply the vertical shifting to perform the function H and the function$f\left(H\right)=f\left(h\right)-100.$

Step-by-step solution

Part a. Step 1. Draw the given graph.

Part a. Step 2. Concept of graph.

Graph is a mathematical representation of a network and it is describe the relationship between line and points.

Part a. Step 3. Answer the question.

The graph indicates that the Luisa’s bungee jump is decrease in every increase of time.

Part b. Step 1. Draw the given graph.

Part b. Step 2. Concept of horizontal shifting.

Horizontal translation refers to the movement towards left or right to the graph of a function by the given units.

Part b. Step 3. Answer the question.

If Luisa goes jump from a 400 ft- high. The new graph that shows the Luisa’s height H(t) after t seconds are,

Part c. Step 1. Draw the graph.

Part c. Step 2. Concept of horizontal shifting.

Horizontal translation refers to the movement towards left or right to the graph of a function by the given units.

Part c. Step 3. Answer the question (c).

We apply the vertical shifting to perform the function H and the function$f\left(H\right)=f\left(h\right)-100.$