A rational function of the form f(x) = (a/(x-1))+k, has a y-intercept of 4 and an x-intercept of 2. What is the value of "a" and "k"?

Answer 1

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The graph of y = f(x) has those given intercepts, not actually the function itself.

The y-intercept is 4.

f(0) = 4

[a/(0 - 1)] + k = 4

-a + k = 4

The x-intercept is 2.

f(2) = 0

[a/(2 - 1)] + k = 0

a + k = 0

-a + k = 4

a + k = 0 (+)

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2k = 4

k = 2

a + 2 = 0

a = -2

Answer 2

4 = -a + k

0 = a + k

a = -2

k = 2

See Graph

https://www.desmos.com/calculator/tcrkhysvxb

Answer 3

y-intercept of 4 --->f(0)=4

and

x-intercept of 2 --->f(2)=0

solve 2 equations for the values of a , k

Answer 4

f(x) = (a/(x-1)) + k

4 = (a/(0-1)) + k ... k = 4 + a

0 = (a/(2-1)) + k ... k = -a <<< add both

. . . . . . . . . . . . . 2k = 4 ... k = 2

.... k = -a .... a = -2