Sketching Graphs of Functions

4.9.3 Sketching Graphs of Functions

4.9.3 • Sketching Graphs of Functions

Activity

Your teacher will show a video of a flag being raised. Function $H$ gives the height of the flag over time. Height is measured in feet. Time is measured in seconds since the flag is fully secured to the string, which is when the video clip begins.

Use your own graph paper to sketch a graph that could represent the function $H$ . Be sure to include a label and a scale for each axis.
Hint: Suggestion for how to set up graph

Compare your answer:

Line graph showing height in feet versus time in seconds. The height increases, plateaus, rises again, stays level, then drops sharply before leveling off, over a total time of 26 seconds.

Self Check

Marcus is going to the library with his friend Monica.

Monica lives between the library and Marcus’s house.
Marcus lives 0.5 mile from Monica, and she lives 0.25 mile from the library.
Marcus walks to Monica’s house in 5 minutes, and he stays there for 15 minutes before they walk together to the library in 3 minutes.

If you were sketching a graph of Marcus’s distance from home in miles with respect to time, in minutes, how would you represent the 15 minutes he was at Monica’s house graphically?

A horizontal line connecting $(5, 0.5)$ and $(20, 0.5)$
A line with a constant rate connecting $(0,0)$ and $(20, 0.5)$
A line with a constant rate connecting $(0,0)$ and $(5, 0.5)$
A vertical line connecting $(5, 0.5)$ and $(5, 20)$

Additional Resources

Graphing Situations as Functions

Example 1

Draw a graph representing a function that describes Sam’s distance from home over an hour.

A: Sam rides his bike to his friend’s house at a constant rate for 20 minutes.

B: Sam plays for 20 minutes at his friend’s house.

C: Sam and his friend bike together to an ice cream shop that is between their houses for 20 minutes.

Here is a sample graph. Notice that the $x$ -axis is labeled “time in minutes” and the $y$ -axis is labeled “distance from home (miles).”

The distance from home is increasing as Sam rides to his friend’s house. While playing at his friend’s house, the distance remained constant and unchanged. When Sam left his friend’s house for the ice cream shop, the distance from home decreased because the shop is in between their houses, so Sam was getting closer to home.

Graph that shows distance from home in miles as a function of time in minutes. x-axis goes from 0 to 60 in increments of 10. y-axis goes from 0 to 3.5 in increments of 0.5. The graph increases linearly from x equals 0 to x equals 20, reaching a distance of 3.25 miles (section a), remains constant from x equals 20 to x equals 40 (section b), and then decreases (section c).

Example 2

Tyler filled up his bathtub, took a bath, and then drained the tub. The function gives the depth of the water $B$ , in inches, $t$ minutes after Tyler began to fill the bathtub.

A blank graph with the y-axis labeled depth (inches) and the x-axis labeled time (minutes). Both axes start at zero and have tick marks, but no data is plotted.

These statements describe how the water level in the tub was changing over time. Use the statements to sketch an approximate graph of the function.

$B (0) = 0$
$B (1) < B (7)$
$B (9) = 11$
$B (10) = B (20)$
$B (20) > B (40)$

A sample graph below meets all of the statements above.

Line graph showing depth in inches over time in minutes. The curve rises steeply, peaks near 15 inches at around 12 minutes, then declines steadily, reaching almost 2 inches at 40 minutes.

Try it

Graphing Situations as Functions

A rock climber begins her descent from a height of 50 feet. She slowly descends at a constant rate for 4 minutes. She takes a break for 1 minute; she then realizes she left some of her gear on top of the rock and climbs more quickly back to the top at a constant rate.

Create a graph representing this situation.

Here is how to graph the situation:

Graph that shows height above the ground in feet as a function of time in minutes. x-axis goes from 0 to 10 in increments of 2. y-axis goes from 0 to 50 in increments of 10. The graph decreases linearly from x equals 0 to x equals 4, remains constant from x equals 4 to x equals 5, and then increases linearly with a steeper slope.