In Exercises 81–94, begin by graphing the absolute value function...

Question

In Exercises 81–94, begin by graphing the absolute value function, f(x) = |x|. Then use transformations of this graph to graph the given function. h(x) = |x + 3| - 2

Accepted Answer

Graph the absolute value function G. X equals the absolute value to x minus six plus three. As the transformation of F. X equals the absolute value of two. X. So our base function is absolute value to X are transformed is two X minus six plus three. I want to check what transformations are on this crap. Let's first check the extra information. The X. Will shift as long as the coefficient of our X. Inside the absolute value bars is equal to one. However we notice here coefficient is actually two because we have two X minus six. Let's take what's inside our absolute value bars two X minus six. Set it equal to zero and then solve for X. This will give us our transformation N. B. X. So add six to both sides. We get two X equals six. That by to get X equals three. We have X equals a positive number. We have a horizontal shift of three to the right now I want to check our vertical shift. You know it's here we have a plus three on the outside this means we have a vertical shift Up by three because it's positive. So you wanna find the graph that shifted to the right by three and shifted up by three. Let's take a look here, graph a is actually shifted to the left three and down three. So it can't be graph a graph B. It's shifted to the left three and up three. We're gonna go to the right so it can't be drafty Graph, seat is shifted to the right three and up three and grab D. Has shifted to the right three and down three. So D. Is wrong, which means the answer to our problem as answers. See Okay. Hope to help you solve the problem. Thank you for watching. Goodbye.

Struggling with College Algebra?

In Exercises 81–94, begin by graphing the absolute value function, f(x) = |x|. Then use transformations of this graph to graph the given function. h(x) = |x + 3| - 2

Watch next

Transformations practice set