Inverse Functions
Transformation of Functions
Equivalent Expressions
Finding Slope from Two Points
Parallel & Perpendicular Slopes
Final Jeopardy
100
What does it mean if f(x) and g(x) are inverses?
y=x
inputs of f(x) are outputs of f-1(x) and outputs of f(x) are inputs of f-1(x)
100
•Describe the transformation of g(x) = f(x) + 3.
Vertical shift up 3 units
100
•Simplify: 3x + 2x.
5x
100
Find slope between (1,2) and (3,6)
m=2
100
Lines that are parallel have ______ slopes
equal
100
Hidden
200
If f(x) = 2x + 6, what is f⁻¹(x)?
f⁻¹(x) = ½x - 3
200
•Describe transformation from f(x) to g(x) = f(x - 2).
•Shift right 2 units.
200
•Factor: x² + 6x + 8.
(x+4)(x+2)
200
•Find slope between (-2,4) and (1,10).
m=2
200
•Lines that are perpendicular have slopes that are ______.
negative reciprocals
300
•A taxi ride costs C = 2.5m + 4. What does the inverse represent?
•The inverse tells how many miles m can be traveled for a given cost C.
300
•If h(x) = -2f(x), what occurs?
•Reflection across x-axis and vertical stretch by 2.
300
2(x + 5) - 3x
•-x + 10
300
Find slope between (5,8) and (5,-2)
undefined
300
•If a line has slope 3, what is perpendicular slope?
m=-1/3
400
•How can you tell if a function’s inverse is also a function?
•If it passes the horizontal line test.
400
•How is y = (x - 4)² + 1 transformed from y = x²?
•Right 4 units, up 1 unit.
400
•Write an equivalent expression for x² - 9.
(x+3)(x-3)
400
Find slope between (-3,7) and (2,-3)
m=-2
400
Line m: y = 2x + 1; parallel line through (0, -4)
y=2x-4
500
•f(x) = 3x - 7 models °F based on °C. What does the inverse represent?
•It converts temperature from °F back to °C.
500
•Describe transformation y = -|x + 5| - 2 from y = |x|.
•Reflect across x-axis, left 5, down 2.
500
Factor: 2x² - 10x
2x(x-5)
500
•Explain what a zero slope means.
horizontal line
500
•p: y = -½x + 6; perpendicular line through (4,1).
y=2x-7