Question

1. use the given table of values to help you select the graph of the absolute value function $f(x) = |x| + 4$.

$x$	$y$
$-1$	$5$
$0$	$4$
$1$	$5$
$2$	$6$

(graph with grid, axes from -5 to 10 on x, and relevant y - axis, showing a v - shaped graph)

Explanation:

Step1: Analyze the vertex from the function

The absolute value function \( f(x) = |x| + 4 \) has its vertex at \( (0, 4) \) because for \( y = |x| + k \), the vertex is at \( (0, k) \) here \( k = 4 \).

Step2: Check the table values

From the table, when \( x = 0 \), \( y = 4 \), which matches the vertex \( (0, 4) \). Also, for \( x=-2 \), \( y = 6 \); \( x = -1 \), \( y = 5 \); \( x = 1 \), \( y = 5 \); \( x = 2 \), \( y = 6 \), which shows the V - shape of the absolute value function shifted up by 4 units. Now, looking at the given graph, we need to check if it has the vertex at \( (0, 4) \) and passes through the points from the table. Wait, the given graph in the image has a vertex at \( (0, - 5) \)? No, wait, maybe there are other graphs (not fully shown). But based on the table, the correct graph should have a vertex at \( (0, 4) \) and pass through \( (-2,6) \), \( (-1,5) \), \( (1,5) \), \( (2,6) \). Assuming the graph with vertex at \( (0, 4) \) (not the one shown with vertex at \( (0, - 5) \)) but since the problem is about selecting the graph, and the table gives us the key points. The correct graph should be the one with vertex at \( (0, 4) \) and the points as per the table. But since the user's image has one graph, maybe the correct one is the one that matches the table. Wait, the given graph in the image has a vertex at \( (0, - 5) \) which is wrong. But maybe there are other graphs. However, based on the table, the function \( f(x)=|x| + 4 \) is a V - shaped graph with vertex at \( (0,4) \) and passing through the points from the table. So the correct graph should have vertex at \( (0,4) \) and the points \( (-2,6) \), \( (-1,5) \), \( (1,5) \), \( (2,6) \) plotted.

Answer:

The graph (not the one shown with vertex at \( (0, - 5) \)) that has a vertex at \( (0, 4) \) and passes through the points \( (-2,6) \), \( (-1,5) \), \( (0,4) \), \( (1,5) \), \( (2,6) \). (If we assume there are multiple graphs, the one with vertex at \( (0,4) \) and the correct points from the table)