Ask a New Question
Menu

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 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.

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.

1 answer

To find the correct graph that represents the function \( f(x) = 12x + 3 \) at the inputs \( -4, -2, 0, 2, \) and \( 4 \), we need to calculate the corresponding outputs for each input:

  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 the points to plot:

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

Given these coordinates, it's important to note that the outputs \( y \) range from about -45 to 51, which suggests a steep positive linear relationship.

Now we can analyze the choices for the graph representation:

  1. The y-axis must cover the range encompassing these values (i.e., from at least -45 to 51).
  2. The x-axis should include values from -4 to 4.

Given the descriptions of the four response images in your query, we only need to check which one has the y-axis ranging below -45 and above 51 or is capable of accommodating these outputs visibly.

Since all options indicate a range from -10 to 10 or 0 to 5, none of them seem to accurately represent the data.

Please ensure to describe the graphs correctly; otherwise, none of the provided responses would match the function values. If there were any dimension or range descriptions missing or misrepresented in the lines plotted, please clarify.