The graph of the function f(x)=a|x-b| on the closed interval [-2,8] What is the value of a?

Question

The graph of the function

f(x)=a|x-b| on the closed interval [-2,8]

What is the value of a?

please show all the steps. Not using calculus. Using the slope formula

Answer 1

Hi Jordan,

By the way this problem reads, I'm guessing that it included a graph.

Without seeing the graph, I can't give you the actual answer, but I can tell you what to look for.

The problem involves a graph of the absolute value function.

The graph of the absolute value function forms a V, or two rays emanating from a point called the Vertex.

The slopes of the rays emanating from the vertex are -1 to the left and 1 to the right.

However, in this problem the function has been shifted "b" units to the right and stretched vertically by a factor of "a". Stretching the graph would change the slopes of the 2 rays to -a on the left and a on the right.

Examine the slopes of the rays, and there's your answer.

EXCEPT THERE'S ONE MORE THING TO CHECK.

Remember, I can't see the graph.

If the "a" is a negative number, then the V would be inverted to look like ∧.

The slope of the ray emanating to the left would be positive while the right half has the negative slope.

In either case, the "a" is the slope of the ray emanating to the right.

I hope this helps.