Below is a graph of the function y = tan ( b x ) y=\tan\left(bx\right) y = tan ( b x ) . Determine the value of b .

Let's see how we can go about solving this problem. Here we're told below is a graph of the function y is equal to the tangent of bx, and we're asked to determine the value of b. Now to solve this problem, I can recognize that b is a period modifier. It's going to change the period of this graph in some kind of way. But how much is it going to change it by? Well, the period for the tangent is equal to pi over b. Well the period is going to be the distance between these asymptotes right here. It's gonna be how the graph repeats, or when the graph repeats on the x axis. And And figure this out, well, I can see that we have a three pi at this final position, and then we have a pi at this first position. And three pi minus pi is two pi. So the distance between these two values on the x axis is two pi. So that means that's what the period is. So now that I've found the period, I can set it equal to the period in this equation. So two pi is going to equal pi over b. And then from here I just need to solve for b using some algebra. So what I'm first going to do is multiply both sides of this equation by b, and that's going to get the b's to cancel on the right side. So we're going to get two pi times b is equal to pi. Now from here what I can do is divide both sides of this equation by two pi. That's going to get the two pi's to cancel on the left side of this equation, leaving me with just b. And then on the right side of this equation, the pi's are going to cancel, so all I'm gonna have is one over two. So b is equal to one half is the solution to this problem. So hope you found this video helpful. Thanks for watching.

12. Trigonometric Functions

Graphs of Other Trigonometric Functions

Business Calculus

12. Trigonometric Functions

Graphs of Other Trigonometric Functions

Struggling with Business Calculus?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Below is a graph of the function $y=\tan\left(bx\right)$ . Determine the value of b.

$b=\frac14$

$b=\pi$

$b=2$

$b=\frac12$

Verified step by step guidance

Step 1: Recall the general form of the tangent function y = tan(bx). The parameter b affects the period of the function. The period of the tangent function is given by the formula Period = π / b.

Step 2: Analyze the graph provided. The graph shows vertical asymptotes at x = π, x = 2π, x = 3π, x = 4π, and x = 5π. This indicates that the period of the function is π.

Step 3: Use the formula for the period of the tangent function, Period = π / b. Since the period is π, set π / b = π.

Step 4: Solve for b. Divide both sides of the equation by π to isolate b. This gives b = 1.

Step 5: Verify the solution by considering the graph. The vertical asymptotes and the periodicity of the function confirm that b = 1 is consistent with the graph provided.