Which equation of a rational function has a hole at x=5 and a y-intercept at (0,7)?

Option C is the answer.

Step-by-step explanation:

We have to find out the equation of a rational function having hole at x=5 and y-intercept at (0,7).

A. y = (x-5)/7x-35 = (x-5)/7(x-5) Here the numerator and denominator have the common factor (x-5) Therefore by

x - 5= 0

x = 5 which represents the hole at x=5 but the equation has no y-intercept.

B. In y = (7x-35)/(x-5)-1

Here 7(x-5)/(x-5) has the common factor (x-5) in numerator and denominator therefore for

x-5=0

x=5 is the hole

By division of 7(x-5)/(x-5) we get remainder 7 but there is already a shift of -1

therefore this equation has (7-1)=6 intercept on y-axis.

C. In y = (7x-35)/(x-5) again numerator and denominator have the common factor (x-5) = 0

or at x=5 the rational function has a hole.

When we divide numerator by denominator the remainder is 7 which is y- intercept is 7.

D. in y = (x-5)/(x-5) +7, x=5 is the hole.

When we divide common factors we get remainder 1 but there is already a shift of +7 so total intercept on y-axis is 1+7 = 8.

So Option C is the right answer.

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.