algebra 1 big ideas math

Question

r(x)=-1/4|x|

btw that is negative 1/4

Answer 1

I am assuming that you are supposed to graph the function, r(x)?

When looking at graphing, you can start by considering what type of function it is. I see r(x) is an absolute value function. Those graphs are generally "V" shaped. The idea for graphing one of these is to find what value of x makes the absolute value portion take on a value of 0. In this case, since it is |x|, this happens when s ix 0. And, if we plug in 0, r(0)=(-1/4)|0|, or r(0)=(-1/4)*0=0. So, this graph has a vertex at the point (0,0)

Then, since that 1/4 is negative, I know that the "V" will open downwards, and the right side will have a slope of -1/4, while the left side has a slope of 1/4, because it becomes a two-part function, where for x's less than 0, it is r(x)=(1/4)x, and x's right of 0, r(x)=(-1/4)x.