Writing Transformations of Functions

Front

Describe the transformation that maps y = g(x) to y = - g(x + 6) - 10

Back

Reflect over x-axis, Shifted down 10 units, Shifted left 6 units

Front

What does the transformation f(x) - 6 represent?

Back

6 Units Down

Front

What transformation does h(\frac{1}{3}x) represent?

Back

Horizontal Stretch by a factor of 3

Front

Which equation describes the transformation of shifting f(x)=x^2 two units right?

Back

(x - 2)^2

Front

Given f(x) = (x-3)^2 + 5, what transformations took place from the original function f(x)?

Back

Right 3 and up 5

Front

What is the effect of a negative sign in front of a function, such as -f(x)?

Back

Reflects the graph over the x-axis.

Front

How does adding a constant to a function, like f(x) + k, affect its graph?

Back

Shifts the graph vertically by k units.

Front

What is the effect of multiplying the input of a function by a factor greater than 1, such as f(kx)?

Back

Horizontal Shrink by a factor of 1/k.

Front

What does the transformation f(x - h) represent?

Back

Shift the graph to the right by h units.

Front

What does the transformation f(x + h) represent?

Back

Shift the graph to the left by h units.