PreCalculus Skills Check, Part 1

Front

What is the definition of a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different parts of its domain.

Front

Back

Front

What does it mean for a function to be undefined at a certain point?

Back

A function is undefined at a certain point if there is no valid output for that input, often due to division by zero or taking the square root of a negative number.

Front

How do you evaluate a piecewise function at a specific point?

Back

To evaluate a piecewise function at a specific point, identify which piece of the function applies to that input and then use the corresponding formula.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in the y-values to the change in the x-values, often represented as m in the equation y = mx + b.

Front

If j(x) = 2x + 1, find j(3).

Back

j(3) = 2(3) + 1 = 7.

Front

What is the formula for finding the slope between two points (x1, y1) and (x2, y2)?

Back

Front

Evaluate f(-4) if f(x) = { 4, x < 0; 2, x >= 0 }.

Back

f(-4) = 4.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

If a function is increasing, what can be said about its slope?

Back

If a function is increasing, its slope is positive.