Question

PRE CALC HELP

Please help me on this question!!! I need to find the value of k

Question: consider the function given below, and solve for the value of K that will make the function continuous for all values in its domain

Answer 1

Answer: k = 4

Reason

Define functions g(x) and h(x) such that:

• g(x) = 5x+k
• h(x) = 9/x

The two functions make up the piecewise function f(x) as shown in the diagram you posted.

• If x < 1, then f(x) = g(x).
• If
  `1 \le \text{x} \le 5`, then f(x) = h(x).

In order for the curves of g(x) and h(x) to connect, we need g(1) = h(1) to be true. The value x = 1 is where the junction point is.

Plug x = 1 into each.

g(x) = 5x+k

g(1) = 5(1)+k

g(1) = 5+k

and

h(x) = 9/x

h(1) = 9/1

h(1) = 9

So,

g(1) = h(1)

5+k = 9

k = 9-5

k = 4 which is the final answer.

This is the value of k where g(1) = h(1) is true and it's the value of k that makes pieces g(x) and h(x) to join up. The diagram below confirms this. I used GeoGebra to make the graph. But Desmos is a great alternative choice.