Linear Transformations and Parent Function

Front

What is the linear parent function?

Back

The linear parent function is f(x) = x, which represents a straight line through the origin with a slope of 1.

Front

What happens to the graph of f(x) = x when it is transformed to g(x) = f(x + 6)?

Back

The graph is shifted left 6 units.

Front

Is the function f(x) = x^2 + 3 linear or nonlinear?

Back

Nonlinear.

Front

If the graph of the parent function f(x) = x is shifted down 7 units, what is the new function?

Back

f(x) = x - 7.

Front

What is the effect of shifting the graph of f(x) = x 5 units to the left and 7 units up?

Back

The new function is f(x) = (x + 5) + 7.

Front

Describe the transformation of g(x) if it is a vertical translation 2 units up of f(x).

Back

g(x) = f(x) + 2.

Front

What does a horizontal translation of a function mean?

Back

It means shifting the graph left or right along the x-axis.

Front

What is the result of reflecting the graph of f(x) = x across the x-axis?

Back

The new function is g(x) = -f(x) or g(x) = -x.

Front

How does a vertical stretch by a factor of 2 affect the function f(x) = x?

Back

The new function is g(x) = 2f(x) or g(x) = 2x.

Front

What is the general form of a linear function?

Back

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