Question

Use the table to answer the question.


Relationship of Values
x f(x)
0 3
1 312
2 4
3 412
This table shows the relationship between x-values and y-values, including fractional values. Which of the following equations describes the function in the table using function notation?

(1 point)
Responses

f(x)=3x+12
f left parenthesis x right parenthesis equals 3 x plus Start Fraction 1 over 2 End Fraction

f(y)=12x+3
f left parenthesis y right parenthesis equals Start Fraction 1 over 2 End Fraction x plus 3

f(x)=12x+3
f left parenthesis x right parenthesis equals Start Fraction 1 over 2 End Fraction x plus 3

f(y)=3x+12
f left parenthesis y right parenthesis equals 3 x plus Start Fraction 1 over 2 End Fraction

Answer 1

f(x) = (1/2)x + 3

Reason: slope = (4 − 3)/(2 − 0) = 1/2 and y-intercept f(0)=3, so f(x) = 1/2 x + 3 (which gives 3.5 at x=1 and 4.5 at x=3).