Download Parameter Changes on the Linear Parent Function

Algebra 1
HS Mathematics
Unit: 04 Lesson: 01
Parameter Changes on the Linear Parent Function
Chart A: The parent function of a linear relationship is y = x. If a coefficient is placed in front of
the x, it causes the steepness or slope of the graph to be changed. Use the graphing calculator to
investigate and describe the changes in steepness “m” has on the graph of the linear parent
function y = x.
Function
Value
of “m” in
y = mx
Up or
down
from left
to right?
Is the
steepness
more, less,
or the
same as
y = x?
x
1
Up
Same
x
-1
Sketch
(both parent
function and given
function on each
coordinate plane)
When x
increases
Coordinates
by 1, y
of the
(increases,
y-intercept
decreases)
by ____
y
10
8
6
4
y=x
2
-10 -8 -6 -4 -2
2
4
6
8 10
2
4
6
8 10
2
4
6
8 10
2
4
6
8 10
-2
Increases
by 1
(0, 0)
-4
-6
-8
-10
y
10
8
6
4
y  x
2
-10 -8 -6 -4 -2
-2
-4
-6
-8
-10
y
10
8
6
4
Increases
by 2
2
y = 2x
-10 -8 -6 -4 -2
x
-2
-4
-6
-8
-10
y
10
8
6
4
2
y = 0.5x
-10 -8 -6 -4 -2
x
-2
-4
-6
-8
-10
©2012, TESCCC
07/12/12
page 1 of 7
Algebra 1
HS Mathematics
Unit: 04 Lesson: 01
Parameter Changes on the Linear Parent Function
Function
Value
of “m” in
y = mx
Sketch
Up or
down
from left
to right?
Is the
steepness
more, less,
or the
same as
y = x?
When x
increases
Coordinates
by 1, y
of the
(increases,
y-intercept
decreases)
by ____
y
10
8
6
4
y  0.5 x
2
-10 -8 -6 -4 -2
2
4
6
8 10
2
4
6
8 10
2
4
6
8 10
x
Down
-2
-4
-6
-8
-10
y
10
8
6
4
2
y = 3.5x
-10 -8 -6 -4 -2
(0, 0)
x
-2
-4
-6
-8
-10
y
10
8
6
4
y  3.5 x
2
-10 -8 -6 -4 -2
x
-2
-4
-6
-8
-10
y
10
8
6
Increases
4
by
3
4
4
y= x
3
2
-10 -8 -6 -4 -2
2
4
6
8 10
x
-2
-4
-6
-8
-10
©2012, TESCCC
07/12/12
page 2 of 7
Algebra 1
HS Mathematics
Unit: 04 Lesson: 01
Parameter Changes on the Linear Parent Function
Function
Value
of “m” in
y = mx
Sketch
Up or
down
from left
to right?
Is the
steepness
more, less,
or the
same as
y = x?
When x
increases
Coordinates
by 1, y
of the
(increases,
y-intercept
decreases)
by ____
y
10
8
6
4
1
y  x
3
2
-10 -8 -6 -4 -2
2
4
6
8 10
2
4
6
8 10
2
4
6
8 10
x
-2
-4
-6
-8
-10
y
10
8
6
4
1
y= x
4
2
-10 -8 -6 -4 -2
x
-2
-4
-6
-8
-10
y
10
8
6
4
y  1.5 x
2
-10 -8 -6 -4 -2
x
-2
-4
-6
-8
-10
©2012, TESCCC
07/12/12
page 3 of 7
Algebra 1
HS Mathematics
Unit: 04 Lesson: 01
Parameter Changes on the Linear Parent Function
Use the information from Chart A to help you answer the following:
1. When “m” is positive, does the line go up or down from left to right? __________
2. When “m” is negative, the line goes ______________ from left to right.
3. When the line is less steep than the graph of y = x what is true about the value of “m”?
4. Does changing the value of “m” cause the line to curve or become a figure other than a line?
5. Does changing the value of “m” change where the line intersects the y-axis? What is the point
of intersection?
6. Predict the graph of y = -5x. Sketch your prediction. Remember to label the x-axis and y-axis.
7. How do you know from the graph if the measure of steepness is positive or negative?
©2012, TESCCC
07/12/12
page 4 of 7
Algebra 1
HS Mathematics
Unit: 04 Lesson: 01
Parameter Changes on the Linear Parent Function
Chart B: The parent function of a linear relationship is y = x. If a number is added to or subtracted
from x, it changes the position of the line with respect to the x and y axes. Use the graphing
calculator to investigate and describe the effect the addition or subtraction of a “b” value has on
the location of the graph of the linear parent function y = x.
Function
Value of
“m” in
y = mx
Sketch
Point of
intersection
on y-axis
Up or
down from
left to
right?
Is the line
more, less,
or the
same
steepness?
y
10
8
6
4
y=x
2
-10 -8 -6 -4 -2
2
4
6
8 10
2
4
6
8 10
2
4
6
8 10
2
4
6
8 10
x
-2
-4
-6
-8
-10
y
10
8
6
4
2
y = x+2
-10 -8 -6 -4 -2
x
-2
-4
-6
-8
-10
y
10
8
6
4
y=x–2
2
-10 -8 -6 -4 -2
x
-2
-4
-6
-8
-10
y
10
8
6
4
y=x–5
2
-10 -8 -6 -4 -2
x
-2
-4
-6
-8
-10
©2012, TESCCC
07/12/12
page 5 of 7
Algebra 1
HS Mathematics
Unit: 04 Lesson: 01
Parameter Changes on the Linear Parent Function
Function
Value of
“m” in
y = mx
Sketch
Point of
intersection
on y-axis
Up or
down from
left to
right?
Is the line
more, less,
or the
same
steepness?
y
10
8
6
4
1
y =x+
2
2
-10 -8 -6 -4 -2
2
4
6
8 10
2
4
6
8 10
2
4
6
8 10
x
-2
-4
-6
-8
-10
y
10
8
6
4
2
y = x +5
-10 -8 -6 -4 -2
x
-2
-4
-6
-8
-10
y
10
8
6
y x
1
2
4
2
-10 -8 -6 -4 -2
x
-2
-4
-6
-8
-10
Use the information from Chart B to help you answer the following:
8. Does addition or subtraction of a value of “b” change where the line intercepts the y-axis?
Explain these changes.
9. Does addition or subtraction of a value of “b” change whether the line goes up or down from
left to right?
10. Does addition or subtraction of a value of “b” change the steepness of the line?
©2012, TESCCC
07/12/12
page 6 of 7
Algebra 1
HS Mathematics
Unit: 04 Lesson: 01
Parameter Changes on the Linear Parent Function
11. Does addition or subtraction of a value of “b” cause the line to curve or become a figure other
than a line?
12. Predict the graph of y = x + 6. Sketch your prediction. Remember to label the x-axis and y-axis.
©2012, TESCCC
07/12/12
page 7 of 7