Master Graphing rational functions Part 1

The video tutorial explains how to graph rational expressions without a calculator by following a seven-step process. It covers identifying symmetry, finding Y and X intercepts, and determining vertical and horizontal asymptotes. The tutorial provides examples to illustrate the process and emphasizes the importance of understanding these steps for accurate graphing.

Why is it important to learn how to graph rational expressions without a calculator?

• Because calculators are unreliable.

• To save time during exams.

• Because calculators are not allowed in any exams.

• To understand the underlying mathematical concepts.

What does it mean if a function is symmetrical about the y-axis?

• The function is identical when both x and y are replaced with their negatives.

• The function is identical when y is replaced with -y.

• The function is identical when x is replaced with -x.

• The function is identical when x is replaced with y.

What is the first step in graphing a rational function?

• Finding the x-intercept

• Identifying symmetry

• Determining the vertical asymptote

• Graphing the function

How do you find the y-intercept of a rational function?

• Set the denominator to zero.

• Set both x and y to zero.

• Set x to zero and solve for y.

• Set y to zero and solve for x.

What is the x-intercept of a function if the equation is 0 = 3x / (x + 1)?

• x = 0

• x = 1

• x = -1

• x = 3

How do you determine the vertical asymptote of a rational function?

• Set both numerator and denominator equal to zero.

• Set the denominator equal to zero.

• Set the numerator equal to zero.

• Set the function equal to zero.

What is the horizontal asymptote if the degrees of the numerator and denominator are the same?

• y = 0

• y = the sum of leading coefficients

• y = the ratio of leading coefficients

• y = 1

Why is it important to choose points to the left and right of vertical asymptotes?

• To ensure the graph is symmetrical.

• To accurately determine the shape of the graph.

• To find the x-intercept.

• To find the y-intercept.

What shape does the graph of a rational function typically resemble?

• A straight line

• A parabola

• A circle

• A hyperbola

What is the final step in graphing a rational function?

• Identifying the horizontal asymptote

• Determining symmetry

• Connecting the points to form the graph

• Finding the x-intercept