parent functions and transformations

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, which serves as a foundation for more complex functions. Examples include linear functions (y = x), quadratic functions (y = x²), and absolute value functions (y = |x|).

Tags

TEKS.MATH.AR.3A

TEKS.MATH.AR.7B

Front

What is the parent function of a linear function?

Back

The parent function of a linear function is y = x.

Tags

TEKS.MATH.AR.3A

TEKS.MATH.AR.7B

Front

What transformation occurs when a function is translated right by 3 units?

Back

The transformation can be represented as f(x) = f(x - 3).

Tags

TEKS.MATH.P.2G

Front

What is the effect of adding a constant to a function, such as f(x) + 2?

Back

Adding a constant to a function results in a vertical translation of the graph. In this case, the graph moves up by 2 units.

Tags

TEKS.MATH.A.3E

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is y = x².

Tags

TEKS.MATH.AR.3A

TEKS.MATH.AR.7B

Front

How does the graph of y = |x| differ from y = x?

Back

The graph of y = |x| is V-shaped and reflects all negative values of x to positive, while y = x is a straight line with a slope of 1.

Tags

TEKS.MATH.2A.6C

Front

What transformation occurs when f(x) is replaced with -f(x)?

Back

This transformation reflects the graph across the x-axis.

Tags

TEKS.MATH.P.2G

Front

What is the parent function of an absolute value function?

Back

The parent function of an absolute value function is y = |x|.

Tags

TEKS.MATH.AR.3A

TEKS.MATH.AR.7B

Front

What does it mean to translate a graph left by 3 units?

Back

Translating a graph left by 3 units means shifting every point on the graph 3 units to the left, represented as f(x) = f(x + 3).

Tags

TEKS.MATH.A.7C

Front

What is the effect of multiplying a function by a negative number, such as g(x) = -f(x)?

Back

Multiplying a function by a negative number reflects the graph across the x-axis.

Tags

TEKS.MATH.A.3E