Chapter 3.8, Problem 41PPS

(a)

To determine

The coordinates of the vertex

Answer to Problem 41PPS

So, therefore $(h,k)$ represents vertex for this graph whose coordinates is $(0,0)$ .

Explanation of Solution

Given information: The equation in terms of x is given as,

  $f(x)=a\left|x-h\right|+k$

The coordinates of the vertex for the general form

  $f(x)=a\left|x-h\right|+k$

  

Vertex is represented by the coordinates $(h,k)$ . In this general form h represents x-intercept and k represents y-intercept.

So, therefore $(h,k)$ represents vertex for this graph whose coordinates is $(0,0)$ .

(b)

To determine

The equationof the line of symmetry for the function’s graph.

Answer to Problem 41PPS

Therefore $x=0$ represents the equation of the line of symmetry for the function’s graph.

Explanation of Solution

Given information: The equation in terms of x is given as,

  $f(x)=a\left|x-h\right|+k$

The equation of the line of the symmetry for the function’s graph is given as,

  

The graph is symmetrical along y-axis since its vertex $(h,k)$ lies at origin.

So, therefore $x=0$ represents the equation of the line of symmetry for the function’s graph.

(c)

To determine

The slopes of the rays that form function’s graph.

Answer to Problem 41PPS

Therefore $a=1$ represents the slopes of the rays that form the function’s graph.

Explanation of Solution

Given information: The equation in terms of x is given as,

  $f(x)=a\left|x-h\right|+k$

The slopes of the rays that form the function’s graph is given as,

Slope is represented by $a$ in the given general form, here $a=1$ .

  

So, therefore $a=1$ represents the slopes of the rays that form the function’s graph.