1. TRANSFORMING LINEAR FUNCTIONS
Describe how changing slope and y-intercept affect the graph of a linear function.

2. Remember:
y = mx+b
slope y-intercept

3. The steepness of a line!!! What does the slope of the line describe?
*The larger the slope the ___________________
steeper the line!
What does the y – intercept of a line describe?
Where the line crosses the y axis!!
*What direction does the y axis go? _______________
Up & Down

4. Look at the functions.
Determine what is the same about them.
Determine what is different about them.
Describe the translation! 1)
y1 →
y2 →
f(x) = 1x + 3
g(x) = 1x + 8
Slope / steepness
The same ___________________________
Different____________________________
Translation: _________________________
y – intercepts
g(x) is shifted 5 units UP from f(x)

5. Look at the functions.
Determine what is the same about them.
Determine what is different about them.
Describe the translation! 2)
y1 →
y2 →
f(x) = 3x + 1
g(x) = 3x - 7
Slope / steepness
The same ___________________________
Different____________________________
Translation: _________________________
y – intercepts
g(x) is shifted 8 units DOWN from f(x)

6. Look at the functions.
Determine what is the same about them.
Determine what is different about them.
Describe the translation! 3)
f(x) = 2x + 5
g(x) = 6x +5
y1 →
y2 →
y-intercepts
The same: ___________________________
Different:____________________________
Translation: __________________________
Slope /steepness
g(x) is 3 times steeper than f(x)

7. Look at the functions.
Determine what is the same about them.
Determine what is different about them.
Describe the translation! 4)
y1 →
y2 →
f(x) = 8x + 1
g(x) = 4x + 1
y-intercepts
The same: ___________________________
Different:____________________________
Translation: __________________________
Slope / steepness
g(x) is ½ as steep as f(x)

8. 5) f(x) = 6x - 2 g(x) = -6x - 2 y1 → y2 →
Look at the functions.
Determine what is the same about them.
Determine what is different about them.
Describe the translation! 5)
f(x) = 6x - 2
g(x) = -6x - 2
y1 →
y2 →
y-intercepts
The same: ___________________________
Different:____________________________
Translation: __________________________
Slopes – 1 positive, 1 negative
g(x) is a reflection of f(x) over the Y AXIS!

9. 6) f(x) = x + 4 g(x) = -x + 4 y1 → y2 →
Look at the functions.
Determine what is the same about them.
Determine what is different about them.
Describe the translation! 6)
f(x) = x + 4
g(x) = -x + 4
y1 →
y2 →
y-intercepts
The same: ___________________________
Different:____________________________
Translation : __________________________
Slopes – 1 positive, 1 negative
g(x) is a reflection of f(x) over the Y AXIS!

10. Look at the functions.
Determine what is the same about them.
Determine what is different about them.
Describe the translation! 7)
y1 →
y2 →
f(x) = x + 4
g(x) = 2x + 7
Nothing
The same: ___________________________
Different:____________________________
Translation : __________________________
Slopes & y-intercepts
g(x) is 2 times as steep as f(x) and shifted UP 3 units.

11. Look at the functions.
Determine what is the same about them.
Determine what is different about them.
Describe the translation! 8)
y1 →
y2 →
f(x) = 3x + 6
g(x) = 9x + 2
Nothing
The same: ___________________________
Different:____________________________
Translation: __________________________
Slopes & y-intercepts
g(x) is 3 times as steep as f(x) and shifted DOWN 4 units

12. g(x) = 2x + 2 g(x) = -4x – 6 g(x) = x – 5 g(x) = -2x + 4
9. What would be the equation of the line f(x) = 2x – 3 shifted up 5 units?
10. What would be the equation of the line f(x) = -4x + 2 shifted down 8 units?
11. What would be the equation of the line f(x) = x – 2 shifted down 3 units.
12. What would be the equation of the line f(x) = 2x + 4 reflected over the y axis?
g(x) = 2x + 2
g(x) = -4x – 6
g(x) = x – 5
g(x) = -2x + 4

13. F(x) is line that goes through the points (-1, -4) and (6, 10).
G(x) is a line that is parallel to f(x) but shifted down 2 units. What is the equation of g(x)?