Evaluating Functions and Expressions

The video tutorial explains how to evaluate functions by substituting different inputs into given equations. It covers basic examples, such as substituting numbers, and progresses to more complex scenarios involving variables. The tutorial also introduces the concept of the difference quotient, demonstrating how to simplify it. Throughout, the video emphasizes the relationship between inputs and outputs in functions.

What is the primary goal when evaluating a function with a given input?

• To find the derivative of the function

• To determine the slope of the function

• To calculate the output corresponding to the input

• To graph the function

If you have the function y = 5x - 2, what is the output when x = 4?

• 22

• 16

• 20

• 18

In function notation, what does f(-4) represent?

• The slope of the function at x = -4

• The y-intercept of the function

• The output of the function when the input is -4

• The integral of the function from 0 to -4

What is the result of evaluating f(k) for the function f(x) = x^2 + 1?

• k^2 - 1

• k^2 + 1

• 2k + 1

• k + 1

When evaluating f(x + h) for f(x) = x^2 - x, what is the first step?

• Multiply x by h

• Subtract h from x

• Add h to the output

• Replace x with x + h

What is the expanded form of (x + h)^2?

• x^2 + h^2

• x^2 + 2h + h^2

• x^2 + 2xh + h^2

• x^2 + 2x + h

What is the purpose of the difference quotient in calculus?

• To find the maximum value of a function

• To solve for the roots of a function

• To calculate the average rate of change of a function

• To determine the y-intercept of a function

In the expression f(x + h) - f(x) / h, what does the h in the denominator represent?

• The change in y

• The y-intercept

• The slope of the tangent line

• The change in x

What is the simplified form of the expression 2hx + h^2 - h divided by h?

• 2x + h - 1

• 2x + h + 1

• 2x - h - 1

• 2x - h + 1

What is the result of subtracting f(x) from f(x + h) in the difference quotient?

• h^2 - x

• x^2 - x

• 2hx + h^2 - h

• x^2 + 2hx + h^2