some math
Describe the transformation from f(x) to g(x) = -f(x-1).
Reflection over x-axis, then shift right by 1.
If g(x) = f(x) - 2, what is the transformation from f(x) to g(x)?
Shifts vertically down by 2 units.
If g(x) = 0.5f(x), what is the transformation?
Vertical compression by a factor of 1/2.
If g(x) = f(-x), what transformation occurs?
Reflection across the y-axis.
In y = af(b(x-h)) + k, a positive h value indicates which transformation?
Horizontal shift right.
When applying multiple transformations to f(x) to get af(b(x-h)) + k, which statement is true about the general order?
Stretches/compressions and reflections are applied before shifts.
In y = af(b(x-h)) + k, a negative k value indicates which transformation?
Vertical shift down.
A function f(x) is reflected across the y-axis and shifted up by 5 units. Which represents g(x)?
g(x) = f(-x) + 5
If g(x) = f(x-4), what is the transformation from f(x) to g(x)?
Shifts horizontally right by 4 units.
Describe the transformation from f(x) to g(x) = -1/2 f(-x).
Vertical reflection, vertical compression by 1/2, horizontal reflection.
If g(x) = f(x) + 5, what is the transformation from f(x) to g(x)?
Shifts vertically up by 5 units.
If g(x) = -f(x), what transformation occurs?
Reflection across the x-axis.
A function f(x) is shifted left by 2 units and stretched vertically by a factor of 3. Which represents the new function g(x)?
g(x) = 3f(x+2)
If g(x) = 3f(x), what is the transformation from f(x) to g(x)?
Stretches vertically by a factor of 3.
Describe the transformation from f(x) to g(x) = f(3x - 6).
Horizontal compression by 1/3, then shift right by 2.
Describe the transformation from f(x) to g(x) = 2f(x) + 1.
Vertical stretch by 2, then shift up by 1.
If g(x) = f(2x), what is the transformation from f(x) to g(x)?
Compresses horizontally by a factor of 1/2.
Describe the transformations from f(x) to g(x) = -2f(0.5(x+3)) - 4.
Vertical reflection, vertical stretch by 2, horizontal stretch by 2, shift left by 3, shift down by 4.
If g(x) = f(0.25x), what is the transformation?
Horizontal stretch by a factor of 4.
If g(x) = f(x+3), what is the transformation from f(x) to g(x)?
Shifts horizontally left by 3 units.
In y = af(b(x-h)) + k, which parameter causes a horizontal compression?
b when |b| > 1.
For g(x) = f(bx), the b parameter controls which type of transformation?
Horizontal stretching, compression, or reflection.
In y = af(b(x-h)) + k, which parameter causes a vertical reflection?
a when a < 0.
A function f(x) is horizontally compressed by a factor of 1/2 and shifted right by 1 unit. Which represents g(x)?
g(x) = f(2(x-1))
If f(x) is transformed to g(x) = f(x+7), what is the value of h in the form f(x-h)?
h = -7