Transformations of Linear Functions

Front

What is the linear parent function?

Back

y = x

Front

What transformation does g(x) = -f(x) represent for the function f(x) = x?

Back

Reflection across the x-axis.

Front

How do you express a horizontal stretch by a factor of 2, a reflection over the x-axis, and a shift down 4 for the function f(x) = x?

Back

-f(1/2x) - 4

Front

If the graph of the parent function f(x) = x is shifted 7 units up and horizontally compressed by a factor of 3, what is the resulting function?

Back

g(x) = f(3x) + 7

Front

Describe the transformation from the graph of f to the graph of g if g is a horizontal translation of f, 4 units left.

Back

The graph of g is shifted 4 units to the left from the graph of f.

Front

What is a vertical shift in the context of function transformations?

Back

A vertical shift moves the graph of a function up or down without changing its shape.

Front

What does a horizontal compression by a factor of k do to the function f(x)?

Back

It compresses the graph of f(x) horizontally, making it narrower by a factor of k.

Front

What is the effect of a reflection over the y-axis on the function f(x)?

Back

It flips the graph of f(x) across the y-axis.

Front

How can you represent a vertical stretch by a factor of 3 for the function f(x)?

Back

By using the function g(x) = 3f(x).

Front

What is the general form of a linear function?

Back

A linear function can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.