Question

use the graph of ( y = f(x) ) to graph the function ( g(x)=f(x)+1 ). choose the correct graph of ( g ) below.

Explanation:

Step1: Identify the transformation

The function \( g(x)=f(x)+1 \) represents a vertical shift of the graph of \( f(x) \) by 1 unit upward.

Step2: Analyze the original graph

From the graph of \( y = f(x) \), we see it's a horizontal line (constant function). Let's find its \( y \)-value. Looking at the grid, the line \( y = f(x) \) is at \( y = 3 \) (since it's midway between \( y = 2 \) and \( y = 4 \), or by counting grid squares: from the \( y \)-axis, the line is at \( y = 3 \)).

Step3: Apply the transformation

For a vertical shift up by 1, the new \( y \)-value for \( g(x) \) is \( 3 + 1 = 4 \). So the graph of \( g(x) \) should be a horizontal line at \( y = 4 \). We then select the graph (among A, B, C, D) that has a horizontal line at \( y = 4 \). (Assuming option C is that graph, so the correct answer is the option with the line at \( y = 4 \), e.g., C.)

Answer:

(Assuming the original graph of \( y = f(x) \) is a horizontal line at \( y = 3 \) (from the grid, since it's between \( y = 2 \) and \( y = 4 \), likely \( y = 3 \)). Then \( g(x)=f(x)+1 \) will be a horizontal line at \( y = 3 + 1=4 \). So we need to identify the graph where the horizontal line is at \( y = 4 \). Let's assume option C (or the one with the line at \( y = 4 \)) is correct. For example, if option C has the horizontal line at \( y = 4 \), then the answer is C. (But since the exact options' graphs aren't fully visible, we'll proceed with the transformation logic. The key is vertical shift up by 1 unit. So the correct graph is the one where each point of \( f(x) \) is shifted up 1 unit.))