Parent Functions and Shifts

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions, which retains the essential characteristics of that family.

Front

Identify the parent function of the absolute value function.

Back

f(x) = |x|

Front

What is the parent function of a quadratic function?

Back

f(x) = x^2

Front

What is the parent function of a linear function?

Back

f(x) = x

Front

What is the parent function of an exponential function?

Back

f(x) = a⋅b^x, where a is a constant and b > 0.

Front

How does the graph of f(x) = |x| look?

Back

The graph is a V-shape that opens upwards, with the vertex at the origin (0,0).

Front

What transformation occurs when you change f(x) to f(x) + k?

Back

The graph of f(x) is translated vertically by k units. If k is positive, it moves up; if negative, it moves down.

Front

What transformation occurs when you change f(x) to f(x - h)?

Back

The graph of f(x) is translated horizontally by h units. If h is positive, it moves to the right; if negative, it moves to the left.

Front

Describe the transformation from y = 2^x to y = 2^{(x + 3)}.

Back

The graph is translated left 3 units.

Front

Describe the transformation from g(x) = f(x) - 5.

Back

The graph of f(x) is translated down 5 units.