0 to -8

Question

1 to -7 1/2
2 to -7
3 to -6 1/2
Which equation describes the function shown in the mapping diagram?

(1 point)
Responses

f(x)=12x−8
f left parenthesis x right parenthesis equals Start Fraction 1 over 2 End Fraction x minus 8

f(x)=8x−12
f left parenthesis x right parenthesis equals 8 x minus Start Fraction 1 over 2 End Fraction

f(y)=8x−12
f left parenthesis y right parenthesis equals 8 x minus Start Fraction 1 over 2 End Fraction

f(y)=12x−8

Answer 1

To determine the function described by the mapping diagram, we'll analyze the given points:

• When \( x = 0 \), \( y = -8 \)
• When \( x = 1 \), \( y = -7.5 \)
• When \( x = 2 \), \( y = -7 \)
• When \( x = 3 \), \( y = -6.5 \)

From the points, we see that as \( x \) increases by 1, \( y \) increases by \( 0.5 \). This indicates a linear relationship between \( x \) and \( y \).

Now let's find the slope (\( m \)) and y-intercept (\( b \)) of the linear function in the form \( y = mx + b \):

1. Finding the slope:

   • The change in \( y \) (rise) when \( x \) increases by 1 (run) is \( 0.5 \).
   • Thus, the slope \( m = 0.5 \).

2. Finding the y-intercept:

   • We can use the point (0, -8) to find the y-intercept.
   • Since at \( x = 0 \), \( y = -8 \), we have \( b = -8 \).

Now, we can write the equation:

\[ y = 0.5x - 8 \]

In the notation that is often used for functions, we can express this as:

\[ f(x) = \frac{1}{2}x - 8 \]

Thus, the correct response from the options provided is:

f(x) = \frac{1}{2}x - 8.