Understanding Functions and Their Properties

This video tutorial covers a comprehensive review of unit 1, focusing on using calculators to find extrema of functions, understanding function boundaries, graphing piecewise functions, identifying discontinuities, determining domains, and exploring function compositions. It also delves into inverse functions and calculating surface area for geometric shapes. The tutorial emphasizes algebraic techniques and graphing skills, providing a detailed walkthrough of each concept.

What is the first step in finding the maximum point of a function using a calculator?

• Estimate the maximum point visually.

• Use the calculator's solve function.

• Directly input the function into the calculator.

• Graph the function and use the trace function.

What does the upper boundary of a function represent?

• The lowest y-value the function can reach.

• The lowest x-value the function can reach.

• The highest x-value the function can reach.

• The highest y-value the function can reach.

When graphing piecewise functions, what does an open circle indicate?

• The function is decreasing at that point.

• The function is increasing at that point.

• The point is not included in the domain.

• The point is included in the domain.

In a piecewise function, what does a closed circle on the graph indicate?

• The point is included in the domain.

• The point is not included in the domain.

• The function is constant at that point.

• The function is undefined at that point.

How can you identify a removable discontinuity in a function?

• It is a point where the function is undefined.

• It can be canceled out in the function's expression.

• It is visible as a gap in the graph.

• It appears as a vertical asymptote.

What must be true for a value to be included in the domain of a square root function?

• The value must be zero or negative.

• The value must be negative.

• The value must be positive.

• The value must be zero or positive.

What is the domain of the function f(x) = √(x - 5)?

• x > 5

• x ≤ 5

• x ≥ 5

• x < 5

What is the domain of the composite function f(g(x)) if g(x) = √(2 - x)?

• x < 2

• x ≥ 2

• x > 2

• x ≤ 2

How do you determine if a function is odd, even, or neither?

• By checking if f(-x) = f(x) for all x.

• By checking if f(x) = x for all x.

• By checking if f(-x) = -f(x) for all x.

• By checking if f(x) = 0 for all x.

What is the range of the function f(x) = √(x - 5)?

• y ≤ 0

• y < 0

• y > 0

• y ≥ 0