Section 1.3 - Shifting, Reflecting, and Stretching Graphs

Section 1.3 covers the shifting, reflecting, and stretching of graphs.

These parent functions provide the basis for a strong understanding of the section:

(This graph uses c=4, though
c is an unknown value until

specified)

Shifting, Reflecting, and Stretching Graphs

1. Adding or subtracting values from the y-coordinate shifts the graph vertically

Adding c shifts the graph up the value of c

Subtracting c shifts the graph down the value of c

Ex:

The graph is shifted up 2 units

2. Adding or subtracting values from the x-coordinate shifts the graph horizontally

Adding c shifts the graph left the value of c

Subtracting c shifts the graph right the value of c

Ex:

The graph shifts 5 units right

3. Multiplying the y-coordinate stretches or compresses the graph vertically

y=c(f(x))

If the value of c is greater than one, the graph is stretched vertically
If the value of c is less than one, the graph is compressed vertically

Ex: If the absolute value of x in multiplied by 4, the graph will be vertically stretched by a factor of 4.

4. Multiplying the x-coordinate stretches or compresses the graph horizontally

y=f(c(x))
If the value of c is greater than one, the graph is compressed horizontally

If the value of c is less than one, the graph is stretched horizontally
Ex: If the square root of x is multiplied by 3, the graph will be horizontally compressed by a factor of 3.

5. Multipying the y-coordinate by a negative number reflects the graph in the x-axis
y=-f(x)
The x values do not change
The y values are opposite of what they were before

Ex:
y=x+2
y=-(x+2)

y=-(x+2) = y=-f(x)

The y values are now opposite of what they were before while the x values do not change

6. Multiplying the x-coordinate by a negative number reflects the graph in the y-axis
y=f(-x)
The x values are opposite of what they were before
The y values do not change
Ex:

y=5x-2

y=5(-1)-2

y=5(-1)-2 = y=f(-x)

The x values are now opposite of what they were before while the y values do not change