Graphing Functions and Intervals

This video tutorial helps students solve an ALEKS problem type involving finding values and intervals where the graph of a function is zero, positive, or negative. The instructor guides through three questions: determining if f(-3) is positive, identifying x values where f(x) equals zero, and finding intervals where f(x) is less than zero. The video uses a graph to visually demonstrate these concepts, emphasizing the importance of understanding function behavior at specific points and intervals.

What is the main focus of the ALEKS problem type discussed in the video?

• Solving equations algebraically

• Determining where a function's graph is zero, positive, or negative

• Finding the maximum value of a function

• Calculating the derivative of a function

How do you find the value of f(-3) using the graph?

• By using the equation of the function

• By looking at the y-axis

• By finding where x equals -3 on the graph

• By calculating the slope at x = -3

What is the value of f(-3) according to the graph?

• Positive

• Undefined

• Zero

• Negative

How many times does f(x) equal zero on the graph?

• Four times

• Three times

• Twice

• Once

At which x-value does f(x) first equal zero?

• x = -3

• x = -2

• x = 1

• x = 4

What is the y-value of f(x) when x = 4?

• Undefined

• Positive

• Zero

• Negative

Which x-value is the last point where f(x) equals zero?

• x = -3

• x = 4

• x = 1

• x = -2

Which x-value is not included in the interval where f(x) is less than zero?

• x = -3

• x = -2

• x = 1

• x = 4

What is the interval notation for x-values where f(x) is less than zero between -3 and -2?

• [-3, -2)

• [-3, -2]

• (-3, -2]

• (-3, -2)

What is the interval notation for x-values where f(x) is less than zero between 1 and 4?

• [1, 4)

• (1, 4)

• [1, 4]

• (1, 4]