To determine whether a graph of a relation is also a function, shayla declares that the  y-axis is a vertical line and counts the number of times that the graph intersects the  y-axis. if the graph has exactly one  y-intercept, shayla concludes that the graph shows a function. in all other cases, she declares that it is not a function.  is shayla applying the vertical line test correctly? a) no, because the  y-axis is a horizontal line. b) no, because using the  y-axis tests only whether  x  = 0 is mapped to multiple values. c) yes, because multiple  y-intercepts represent multiple  x-values being mapped to  y  = 0.d) yes, because the  y-axis represents all vertical lines of the  x-values.

Option B is the right answer.

Step-by-step explanation:

To check whether a graph of a relation is a function or not we can use vertical line test.

The vertical line test for a function says that at any point on its domain, the vertical line through that point must intersect the curve only once.  Even is there is one exception to this rule, the graph cannot represent a function.

Keeping this in mind, we can say what Shayla is doing is a wrong method as she test for vertical test only at a particular value of x=0 and not throughout the domain.

Hence option B is right

B) No, because using the y-axis tests only whether x = 0 is mapped to multiple values.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

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step-by-step explanation: