Question

Given: f(x)=7|x-3|-4

Which way does the graph open?

What is the vertex of the graph?

Is the graph wider, narrower, or the same width as the graph of y=|x|?

Answer 1

up

Answer 2

The expression within the absolute value sign, "x - 3" is never negative, so to answer the first question, you can look at what is called the end behaviors: as x is large positive and large negative. In either direction, "y" will be getting larger positive, so the graph opens upwards.

The vertex of the graph is where "x - 3" is smallest and that is at x = 3. The corresponding "y" value at that "x" is -4, so the vertex is (3, -4).

This graph is narrower than y = |x| as is evidenced by looking at the graph at x > 3. Here, the equation becomes:

y = 7(x - 3) - 4 -> y = 7x - 25 and we see a slope of "7". Same in the opposite direction at x < 3 with slope of -7.

Answer 3

Good luck to you in all of your studies! @AshleyStew