kyla
The algebraic method for finding an inverse function involves interchanging x and y, then solving for which variable?
y
In the point transformation rule (x/b + h, ay + k), which part corresponds to the horizontal translation?
+ h
What is the graphical relationship between a function and its inverse?
Reflection across the line y = x.
Given the points (-1, -5), (0, -3), (1, -1) on y = f(x), what are the corresponding points on its inverse?
(-5, -1), (-3, 0), (-1, 1)
A point (2, 4) on y = f(x) is transformed by y - 1 = f(x - 3). What are the new coordinates of the point?
(5, 5)
If a function maps x to y, its inverse maps y back to what variable?
x
Identify the value of 'b' in the equation y + 2 = f(3x).
3
What notation is used to represent the inverse of a function f(x)?
f⁻¹(x)
If the parameter 'a' is -1, what transformation occurs?
Reflection in x-axis
How does the parameter 'h' affect the graph of a function y = f(x) in the general form y - k = af(b(x - h))?
Shifts horizontally h units. Right if h > 0, Left if h < 0.
Given the function y - 1 = -2f(x + 1), what is the 'a' value?
-2
Given the function y - 5 = 3f(x - 2), what is the value of 'k'?
5
In the transformation y - k = af(b(x - h)), if 'b' is 1/2, what is the effect on the graph?
Horizontal stretch by factor of 2
The graph of an inverse function is a reflection of the original function across which line?
y = x
If y = f(x) = x + 7, which function represents its inverse?
f⁻¹(x) = x - 7
What is the general form for a transformed function?
y - k = af(b(x - h))
Which parameter in y - k = af(b(x - h)) causes a reflection in the y-axis?
A negative value for b.
Find the inverse of the function y = x + 5.
f⁻¹(x) = x - 5
When combining transformations, what type of transformations should be applied first?
Stretches/compressions/reflections
For a point (x, y) on y = f(x), how does a vertical translation of 'k' units affect the y-coordinate?
y becomes y + k
In the general form y - k = af(b(x - h)), what type of transformation is associated with the parameter 'a'?
Vertical Stretch/Compression & Reflection
For the function y - 3 = 0.5f(x + 4), describe the vertical stretch/compression.
Vertical compression by a factor of 0.5
Which function below is the inverse of y = (x - 2) / 3?
f⁻¹(x) = 3x + 2
What is the final step when algebraically determining the equation of the inverse of a function?
Write the inverse function notation.
For the function f(x) = 3x - 1, find f⁻¹(x).
f⁻¹(x) = (x + 1) / 3
If a point on the original function is (m, n), what are the coordinates of the corresponding point on its inverse?
(n, m)
What is the first algebraic step to find the inverse of a function y = f(x)?
Interchange x and y in the original equation.
The inverse of the function y = x is itself. Is this statement consistent with the definition of inverse functions?
Yes.
Consider the function y = -4f(0.5(x + 2)) - 3. Which parameter indicates a vertical reflection?
a = -4
If a point (3, 7) is on the graph of y = f(x), what point is on the graph of its inverse, y = f⁻¹(x)?
(7, 3)