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Algebra 1

4.9.3 Sketching Graphs of Functions

Algebra 14.9.3 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 HH 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.

  1. Use your own graph paper to sketch a graph that could represent the function HH. Be sure to include a label and a scale for each axis.

    Hint: Suggestion for how to set up graph

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?

  1. A horizontal line connecting ( 5 , 0.5 ) and ( 20 , 0.5 )
  2. A line with a constant rate connecting ( 0 , 0 ) and ( 20 , 0.5 )
  3. A line with a constant rate connecting ( 0 , 0 ) and ( 5 , 0.5 )
  4. 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 xx-axis is labeled “time in minutes” and the yy-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.

Example 2

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

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

A sample graph below meets all of the statements above.

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.

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