Question

you are given a table showing input and output values for a given function ( y_1 = f(x) ). using this table, find (if possible) (a) the x - intercept of the graph of ( y = f(x) ), (b) the y - intercept of the graph of ( y = f(x) ), and, (c) the solution to the equation ( f(x)=0 ).
(a) what is the x - intercept? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
( \bigcirc ) a. ( x = square )
( \bigcirc ) b. there is no x - intercept.
(b) what is the y - intercept? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
( \bigcirc ) a. ( y = square )
( \bigcirc ) b. there is no y - intercept.
(c) what is the solution to ( f(x)=0 )? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
( \bigcirc ) a. ( x = square )
( \bigcirc ) b. there is no solution.

Explanation:

Step1: Identify x-intercept

The x-intercept is the x-value where $y_1=0$. From the table, when $y_1=0$, $x=-2$.

Step2: Identify y-intercept

The y-intercept is the y-value where $x=0$. From the table, when $x=0$, $y_1=-46$.

Step3: Solve $f(x)=0$

$f(x)=0$ corresponds to the x-value where $y_1=0$, which is $x=-2$.

Answer:

(a) A. $x=-2$
(b) A. $y=-46$
(c) A. $x=-2$