Exercise 52 Page 604

a The

x -

and

y -

intercepts are points where the graph crosses the

x -

and

y -

axis, respectively. Let's identify them on the given graph.

Now we can determine the coordinates of these intercepts.

As we can see, the graph crosses the $x -$ axis at the points $(- 2, 0)$ and $(0, 0) .$ Notice that at the point $(0, 0)$ the graph crosses not only the $x -$ axis, but also the $y -$ axis. Thus the $x -$ intercepts are $- 2$ and $0,$ and the $y -$ intercept is $0 .$

b Let's identify the points where the given function crosses either the

x -

or the

y -

axis on the graph.

Now we can determine the coordinates of this point.

As we can see, the graph crosses the $x -$ axis at the points $(- 3, 0)$ and $(5, 0) .$ Thus the $x -$ intercepts are $- 3$ and $5 .$ We can also notice that the graph intercepts the $y -$ axis at the point $(0, 3),$ so the $y -$ intercept is $3 .$

c We will identify the

x -

and

y -

intercepts of the given relation one at a time.

x	$- 3$	$- 2$	$- 1$	$0$	$1$	$2$	$3$
y	$8$	$3$	$0$	$- 1$	$0$	$3$	$8$

Finding the $x -$ intercept

Think of the point where the graph of a relation crosses the $x -$ axis. The $y -$ value of that $(x, y)$ coordinate pair is $0,$ and the $x -$ value is the $x -$ intercept. To find the $x -$ intercept of the relation, we need to find the points where the $y -$ value is $0 .$

x	$- 3$	$- 2$	$- 1$	$0$	$1$	$2$	$3$
y	$8$	$3$	$0$	$- 1$	$0$	$3$	$8$

We can see that the $x -$ intercepts are $- 1$ and $1 .$

Finding the $y -$ intercept

Let's use the same concept to find the $y -$ intercept. Consider the point where the graph of the relation crosses the $y -$ axis. The $x$ -value of the $(x, y)$ coordinate pair at the $y -$ intercept is $0 .$ Therefore, we need to find the point where the $x -$ value is $0 .$