Functions and Linear Transformations

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions, which retains the essential characteristics of that family.

Front

How does shifting a function vertically affect its equation?

Back

Shifting a function vertically involves adding or subtracting a constant to/from the function's output (y-value). For example, f(x) + k shifts the graph up by k units, while f(x) - k shifts it down by k units.

Front

What does the equation y = f(x - c) represent?

Back

The equation y = f(x - c) represents a horizontal shift of the parent function to the right by c units.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

If f(x) = x, what is the equation of the function shifted down 2 units?

Back

f(x) = x - 2.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, resulting in a downward slant of the line.

Front

How do you determine the range of a function?

Back

The range of a function is determined by the set of all possible output values (y-values) that the function can produce.

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.

Front

What does the equation y = 3x + 2 represent?

Back

This equation represents a linear function with a slope of 3 and a y-intercept of 2.

Front

If the graph of f(x) = x is shifted left by 4 units, what is the new equation?

Back

The new equation is f(x) = x + 4.