Transformations of parent functions

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, from which other functions can be derived by transformations such as translations, reflections, and stretches.

Front

What does it mean to reflect a function over the x-axis?

Back

Reflecting a function over the x-axis means to invert the output values (y-values) of the function, resulting in a new function that is the negative of the original.

Front

How does a vertical stretch affect a function?

Back

A vertical stretch multiplies the output values of a function by a factor greater than 1, making the graph of the function steeper.

Front

What is the effect of translating a function left or right?

Back

Translating a function left or right involves shifting the graph horizontally. A positive shift moves the graph to the left, while a negative shift moves it to the right.

Front

What is the general form of an absolute value function?

Back

The general form of an absolute value function is y = a|x - h| + k, where (h, k) is the vertex and 'a' determines the vertical stretch or compression.

Front

What does the term 'quadratic function' refer to?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form y = ax² + bx + c, where a, b, and c are constants.

Front

How do you identify a vertical shift in a function?

Back

A vertical shift occurs when a constant is added to or subtracted from the function's output. For example, y = f(x) + k shifts the graph up by k units if k > 0 and down if k < 0.

Front

What is the effect of a horizontal stretch on a function?

Back

A horizontal stretch occurs when the input values of a function are multiplied by a factor less than 1, making the graph wider.

Front

What is the equation of a square root function?

Back

The general form of a square root function is y = a√(x - h) + k, where (h, k) is the vertex and 'a' affects the vertical stretch.

Front

How do you determine the vertex of a quadratic function?

Back

The vertex of a quadratic function in standard form y = ax² + bx + c can be found using the formula x = -b/(2a) to find the x-coordinate, then substituting back to find the y-coordinate.