Question

(02.05 lc)
the graphs of functions f(x) and g(x)=f(x)+k are shown:
what is the value of k?
o a k = -2
o b k = 2
o c k = -4
o d k = 4

Explanation:

Step1: Identify y - intercepts

The y - intercept of \(f(x)\) is \(- 2\) (where the graph of \(f(x)\) crosses the y - axis), and the y - intercept of \(g(x)\) is \(2\).

Step2: Use the relationship \(g(x)=f(x)+k\)

At \(x = 0\), \(g(0)=f(0)+k\). Substituting \(g(0) = 2\) and \(f(0)=-2\) into the equation \(g(0)=f(0)+k\), we get \(2=-2 + k\).

Step3: Solve for \(k\)

Add 2 to both sides of the equation \(2=-2 + k\): \(k=2 + 2=4\).

Answer:

d. \(k = 4\)