Function Transformation Test

Front

What is an absolute maximum in a function?

Back

An absolute maximum is the highest point over the entire domain of a function. It is the largest value that the function attains.

Front

How do you find the transformed function f(x-8) if f(x) = 3x + 5?

Back

To find f(x-8), substitute (x-8) into the function: f(x-8) = 3(x-8) + 5 = -3x - 19.

Front

What is the x-intercept of a function?

Back

The x-intercept is the point where the graph of the function crosses the x-axis, meaning the value of y is 0.

Front

If y = x^2 represents a parabola, what does y = -x^2 represent?

Back

y = -x^2 represents a downward-opening parabola, which is a reflection of y = x^2 across the x-axis.

Front

What defines a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

What is the vertex of a parabola represented by the equation y = ax^2 + bx + c?

Back

The vertex can be found using the formula x = -b/(2a) and then substituting back to find y.

Front

What effect does changing the value of 'a' in y = ax^2 have on the graph?

Back

Changing 'a' affects the width and direction of the parabola. If 'a' is positive, it opens upwards; if negative, it opens downwards.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

How does a vertical shift affect the graph of a function?

Back

A vertical shift moves the graph up or down without changing its shape. For example, y = f(x) + k shifts the graph up by k units.

Front

What is a horizontal shift in function transformation?

Back

A horizontal shift moves the graph left or right. For example, y = f(x - h) shifts the graph right by h units.