It increases the steepness if the stretch factor is greater than 1 and decreases it if the factor is between 0 and 1.

It shifts the x-intercepts by the same amount as the horizontal shift. A shift to the right increases the x-intercept values, and a shift to the left decreases them.

It changes the sign of all y-values, flipping the graph over the x-axis.

It decreases the period by the compression factor, making the function oscillate more rapidly.

It's a reflection of $y = f(x)$ over the y-axis.

The entire graph is shifted up or down without changing its shape.

The x-coordinate of the vertex shifts by the same amount as the horizontal shift.

It reduces the maximum and minimum values by the compression factor.

If the original function was even (symmetric about the y-axis), the reflection doesn't change the graph. If it was odd (symmetric about the origin), the reflection changes the sign of the function.

It expands the domain by the stretch factor.

Shifting a function's graph up or down by adding/subtracting a constant.

Shifting a function's graph left or right by adding/subtracting a constant to the input.

Stretching or shrinking a function's graph vertically by multiplying the function by a constant.

Stretching or shrinking a function's graph horizontally by multiplying the input by a constant.

Flipping a function's graph over the x-axis, achieved by multiplying the function by -1.

Flipping a function's graph over the y-axis, achieved by replacing x with -x.

Altering the graph of a function by shifting, stretching, shrinking, or reflecting it.

Stretching or compressing the graph of a function either vertically or horizontally.

$g(x) = a cdot f(bx + h) + k$

A transformation that multiplies all y-values of a function by a factor greater than 1, making the graph taller.

$g(x) = f(x) + k$

$g(x) = f(x + h)$

$g(x) = af(x)$

$g(x) = f(bx)$

$g(x) = -f(x)$

$g(x) = f(-x)$

$g(x) = a cdot f(bx + h) + k$

$g(x) = 3f(x)$

$g(x) = f(2x)$

$g(x) = f(x-5)$