Evaluating Piecewise Functions Effectively

This video tutorial covers the concept of piecewise functions, explaining how they are defined by multiple equations, each applicable to a different part of the domain. It includes a review of graphing piecewise functions and evaluating algebraic functions. The tutorial provides guided practice on evaluating piecewise functions using process of elimination to determine which part of the function to use based on the given x value. The lesson concludes with an independent practice exercise to reinforce the learning objectives.

What is a piecewise function?

• A function defined by a single equation.

• A function defined by two or more equations, each applying to a different part of its domain.

• A function that is always linear.

• A function that only applies to positive values of x.

Which of the following is true about the piecewise function f(x) = -x - 1 for x ≤ 2?

• It has a slope of 1.

• It has a y-intercept of -1.

• It is a quadratic function.

• It is defined for x > 2.

When graphing the function f(x) = 1/2x - 2 for x > 2, why don't we see the y-intercept?

• Because the y-intercept is not part of the domain.

• Because the function is not linear.

• Because the y-intercept is at x = 2.

• Because the y-intercept is at x = 0, which is not included in the domain.

How do you evaluate the function f(x) = 2x - 4 for x = 6?

• Replace x with 6 and solve.

• Replace x with 4 and solve.

• Replace x with 2 and solve.

• Replace x with -4 and solve.

What is the value of f(6) for the function f(x) = 2x - 4?

• 8

• 10

• 12

• 4

In the guided practice, which piece of the function do we evaluate for f(7) when f(x) = -3x for x > 1?

• None of the above

• The piece for x ≤ -2

• The piece for x > 1

• The piece for -2 < x ≤ 1

What is the value of f(7) for the function f(x) = -3x?

• -3

• -21

• 21

• 3

Which inequality does x = -2 satisfy for the function f(x) = x^2 - 5?

• x = 0

• x > -4

• x ≤ -4

• x < -2

What is the value of f(-2) for the function f(x) = x^2 - 5?

• -4

• 4

• -1

• 1

What is the final value of f(-2) for the function f(x) = x^2 - 5?

• 1

• 2

• -1

• 0