Question

Use the graph of y equals f left parenthesis x right parenthesis to graph the function g left parenthesis x right parenthesis equals f left parenthesis x right parenthesis plus 3.
y = f(x)
-6
-4
-2
2
4
6
-6
-4
-2
2
4
6
x
y



A coordinate system has a horizontal x-axis labeled from negative 6 to 6 in increments of 1 and a vertical axis labeled y equals f(x) from negative 6 to 6 in increments of 1. A graph is a series of two connected line segments. The line segments have endpoints plotted at the following coordinates: (negative 2, negative 1); (0, negative 1); (2, negative 1).
.
.
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Question content area right
Part 1
Choose the correct graph of g below.
A.
-6
6
-6
6
x
y



A coordinate system has a horizontal x-axis labeled from negative 6 to 6 in increments of 1 and a vertical y-axis labeled from negative 6 to 6 in increments of 1. A graph is a series of two connected line segments. The line segments have endpoints plotted at the following coordinates: (negative 2, 2); (0, 2); (2, 2).
B.
-6
6
-6
6
x
y



A coordinate system has a horizontal x-axis labeled from negative 6 to 6 in increments of 1 and a vertical y-axis labeled from negative 6 to 6 in increments of 1. A graph is a series of two connected line segments. The line segments have endpoints plotted at the following coordinates: (negative 5, negative 1); (negative 3, negative 1); (negative 1, negative 1).
C.
-6
6
-6
6
x
y



A coordinate system has a horizontal x-axis labeled from negative 6 to 6 in increments of 1 and a vertical y-axis labeled from negative 6 to 6 in increments of 1. A graph is a series of two connected line segments. The line segments have endpoints plotted at the following coordinates: (negative 2, negative 4); (0, negative 4); (2, negative 4).
D.
-6
6
-6
6
x
y

Answer 1

To determine the graph of \( g(x) = f(x) + 3 \) from \( f(x) \), we need to apply the transformation of adding 3 to the output values of \( f(x) \). This means that every point on the graph of \( f(x) \) will be shifted vertically upward by 3 units.

From the description of \( f(x) \), it has the following points:
- \( f(-2) = -1 \)
- \( f(0) = -1 \)
- \( f(2) = -1 \)

When we shift these points up by 3 units to find the corresponding points for \( g(x) \):
- \( g(-2) = f(-2) + 3 = -1 + 3 = 2 \)
- \( g(0) = f(0) + 3 = -1 + 3 = 2 \)
- \( g(2) = f(2) + 3 = -1 + 3 = 2 \)

So the new points for \( g(x) \) are:
- \( (-2, 2) \)
- \( (0, 2) \)
- \( (2, 2) \)

Now, let's analyze the options provided:

- **Option A**: Contains points \( (-2, 2) \), \( (0, 2) \), and \( (2, 2) \) - This matches our calculation.
- **Option B**: Has endpoints at \( (-5, -1) \), \( (-3, -1) \), and \( (-1, -1) \) - This does not match.
- **Option C**: Shows points \( (-2, -4) \), \( (0, -4) \), and \( (2, -4) \) - This does not match.
- **Option D**: No specific points provided - Cannot be determined.

The correct graph for \( g(x) = f(x) + 3 \) is **Option A**.