Parent functions and transformations 1st sem final review

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, quadratic, cubic, and absolute value functions.

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is f(x) = x².

Front

How does the graph of g(x) = x² - 5 differ from the parent function f(x) = x²?

Back

The graph of g(x) = x² - 5 is the same as the graph of f(x) = x², but it is translated downward by 5 units.

Front

What transformation does the equation y = (x + 5)² represent?

Back

The equation y = (x + 5)² represents a horizontal translation of the parent function f(x) = x² to the left by 5 units.

Front

What is the effect of adding a constant to a quadratic function?

Back

Adding a constant to a quadratic function translates the graph vertically. For example, y = x² + 5 shifts the graph up by 5 units.

Front

What is the parent function of a linear function?

Back

The parent function of a linear function is f(x) = x.

Front

What transformation does the equation g(x) = (x - 5)² represent?

Back

The equation g(x) = (x - 5)² represents a horizontal translation of the parent function f(x) = x² to the right by 5 units.

Front

What is the parent function of an absolute value function?

Back

The parent function of an absolute value function is f(x) = |x|.

Front

How do you identify a quadratic function from its equation?

Back

A quadratic function can be identified by its highest degree being 2, typically in the form f(x) = ax² + bx + c, where a ≠ 0.

Front

What is the effect of a negative sign in front of a quadratic function?

Back

A negative sign in front of a quadratic function, such as g(x) = -x², reflects the graph across the x-axis.