Graphs with Linear “Parts” Practice
Name______________ANSWERS______________________________
Directions: Please show your work!
1. Given:
  x  3; 0  x  5
y
2 x  12; 5  x  8
a) Graph the function.
b) State the domain (the x-values used).
Domain: [0,8) All x's greater than or equal to 0 and less than 8.
2.
Write a piecewise definition in the form “ y = ”
for the graph shown at the right.
(Indicated points have integer co0rdinates.)
y
3.
 x  1; 4  x  1

  x; 1  x  3
 2; 4  x  1
Given: y  
2; 1  x  4
a) Graph the function.
b) State the domain (the x-values used).
Domain: [-4,-1) U (-1,4] All x's greater than or equal to -4 and less than or
equal to 4, but not equal to -1.
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Dylan rides his motorcycle from his home to his
friend's home 125 miles away. The graph at the
right shows his journey.
a) Write a story that will represent his trip.
b) State the fastest average speed he maintained
for at least one hour.
a) Story: Dylan leaves his home and drives for one hour
averaging 25 mph to leave his city. When he leaves the city
limits, he travels for one hour averaging 50 mph. He then
stops for lunch for one hour. After lunch, he enters his
friend's city limits and travels for 2 hours averaging 25 mph until he arrives at his friend's
home. b) Fastest average speed he maintained for at least 1 hour was 50 mph.
5. It takes Ariel 60 minutes to reach the hiking team's
campsite, following a trail depicted in the graph at
the right.
a) Write a story that will describe this hiking journey.
b) What is the change in the elevation between Ariel's
starting point and the campsite?
a) Story: Starting at 5 feet above sea level, Ariel begins the
hike by reading her map and rearranging her pack for 10
minutes. She then hikes up a small hill for 10 minutes,
reaching level ground where she walks for another 10 minutes.
She goes down a small hill for 10 minutes before climbing a steep
hill for 10 minutes reaching 25 feet above sea level. After an additional 10 minute walk on
level ground she arrives at the campsite. b) The change in elevation between Ariel's starting location and the campsite is 20 feet.
x  1
 x  1;
Given the graph : y  
( x  1); x  1
a) What is the rate of change of the graph on the interval
where x > -1?
The rate of change (the slope) when x > -1 is +1.
6.
b) What is the rate of change of the graph on the interval
where x < -1?
The rate of change when x < -1 is -1.
c) At what x-value(s) will the y-value be +3?
The y-value is +3 when the x-value is either +2 or -4.
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Lynn usually has her bangs cut every three months. The
graph at the right shows the growth of her bangs over
the past year.
a) Write a story to describe her bang lengths for the past
year.
b) Does the graph indicate that Lynn's bangs continue to
grow at a consistent rate? Explain.
a) Story: Lynn has her bangs cut to a length of 2 inches each
time they are cut. From Jan. to March her bangs grew 3 inches
and the bangs were cut at the beginning of March. She missed
her next 3 month cut and the bangs grew 6 inches until her cut in Sept. She then returned to
her 3-month cutting schedule. b) Yes, her bangs appear to be growing at a consistent rate since the slopes of all of the
graph segments are the same, an average rate of 1 inch per month.
8.
The chart at the right shows the average
yearly car prices from 1910 to 1920.
a) What could possibly have caused
the drastic drop in car prices starting
in 1914?
World War 1 b) What was the percentage of decrease
in the average price of a car from 1914
to 1916? From 1914 to 1916, the price dropped from
$2500 to $1600, or $900. n% of 2500 = 900 n% = 36%
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