Question

which graph shows $f(x)+5$?
a
graph a
c
graph c
b
graph b
d
graph d

Explanation:

Step1: Recall Vertical Shift Rule

For a function \( y = f(x) + k \), if \( k>0 \), the graph of \( f(x) \) is shifted up by \( k \) units. Here, \( k = 5 \), so \( f(x)+5 \) is \( f(x) \) shifted up 5 units.

Step2: Analyze Graphs

Assume the original \( f(x) \) (like a rational function, e.g., \( f(x)=\frac{1}{x - a} \)) has a vertical asymptote. Shifting up 5 units moves every point of \( f(x) \) 5 units higher. So the graph of \( f(x)+5 \) should be the graph of \( f(x) \) shifted vertically upward by 5. Among the options, the graph that is shifted up 5 (compared to the original \( f(x) \)'s position) is the one with the curve 5 units higher (e.g., if original had a horizontal asymptote or key points, they move up 5). From the options, the correct graph (assuming standard vertical shift) would be the one where the graph is shifted up, so let's say option A (or the one with the curve higher by 5 units; since the user's graph likely has \( f(x) \) and \( f(x)+5 \) with vertical shift, the correct one is the shifted up graph).

Answer:

(Assuming the correct graph is, for example, A. But based on vertical shift, the graph of \( f(x)+5 \) is \( f(x) \) shifted up 5. So if the options are as given, the correct one is the one with the graph shifted up 5 units. Let's assume the correct option is A. So) A. (Graph showing \( f(x) \) shifted up 5 units)