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Use input-output tables to determine which graph accurately represents the function f(x)=12x+3

with inputs of −4
, −2
, 0, 2, and 4.(1 point)
Responses

Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.

Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.

Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from 0 to 7 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from 0 to 7 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1.

Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
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User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
3 hours ago

To determine which graph accurately represents the function \( f(x) = 12x + 3 \) for the given input values of \( x = -4, -2, 0, 2, 4 \), we first need to compute the corresponding output values (i.e., function values) using the equation.

1. For \( x = -4 \):
\[
f(-4) = 12(-4) + 3 = -48 + 3 = -45
\]

2. For \( x = -2 \):
\[
f(-2) = 12(-2) + 3 = -24 + 3 = -21
\]

3. For \( x = 0 \):
\[
f(0) = 12(0) + 3 = 0 + 3 = 3
\]

4. For \( x = 2 \):
\[
f(2) = 12(2) + 3 = 24 + 3 = 27
\]

5. For \( x = 4 \):
\[
f(4) = 12(4) + 3 = 48 + 3 = 51
\]

Now we have our input-output pairs:

- \( (-4, -45) \)
- \( (-2, -21) \)
- \( (0, 3) \)
- \( (2, 27) \)
- \( (4, 51) \)

Next, we can plot these points and find the appropriate graph based on the described characteristics:

- The x-values range from -4 to 4.
- The corresponding y-values range from -45 to 51, which is much larger than the -10 to 10 range indicated in some of the responses.

Given this significant range for the y-values, the graph that accurately captures the data must be able to show values beyond -10 and 10 on the y-axis.

From your description, the most suitable response seems to be the one that has an x-axis range from -4 to 4 and a y-axis that can accommodate values below -10 and above 10, ultimately reflecting this steep function's growth and decline accurately.

Please select the option that corresponds to these criteria for the graph of \( f(x) = 12x + 3 \).