Transformations of Linear Functions

Front

What is a vertical translation of a function?

Back

A vertical translation of a function occurs when the entire graph of the function is shifted up or down by a certain number of units. For example, if f(x) is translated vertically up by 2 units, the new function is f(x) + 2.

Front

What happens to the graph of f(x) when it is transformed to g(x) = -f(x)?

Back

The graph of f(x) is reflected across the x-axis when transformed to g(x) = -f(x). This means that all y-values of f(x) are multiplied by -1.

Front

How does the equation y = f(x) + c affect the graph of f(x)?

Back

The equation y = f(x) + c shifts the graph of f(x) vertically. If c is positive, the graph shifts up by c units; if c is negative, it shifts down by |c| units.

Front

What is a horizontal translation of a function?

Back

A horizontal translation of a function occurs when the graph of the function is shifted left or right. For example, g(x) = f(x - 4) translates the graph of f(x) 4 units to the right.

Front

What does the transformation g(x) = f(x + 3) represent?

Back

The transformation g(x) = f(x + 3) represents a horizontal translation of the graph of f(x) 3 units to the left.

Front

What is the effect of multiplying a function by a negative number?

Back

Multiplying a function by a negative number reflects the graph across the x-axis. For example, g(x) = -f(x) reflects the graph of f(x) over the x-axis.

Front

What does a vertical stretch of a function mean?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1. For example, g(x) = 2f(x) stretches the graph of f(x) vertically by a factor of 2.

Front

What is the parent function of linear functions?

Back

The parent function of linear functions is f(x) = x, which represents a straight line passing through the origin with a slope of 1.

Front

How does the transformation g(x) = f(x) - 5 affect the graph of f(x)?

Back

The transformation g(x) = f(x) - 5 shifts the graph of f(x) down by 5 units.

Front

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

Back

A horizontal compression occurs when the input values of a function are multiplied by a factor greater than 1. For example, g(x) = f(2x) compresses the graph of f(x) horizontally by a factor of 2.