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

Remember: y = mx+b slope y-intercept

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

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)

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)

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)

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)

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!

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!

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.

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

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)?