Respuesta :
if x increases by 51, f (x) increases by 9.
Step-by-step explanation:
Given function:
[tex]f(x)=\frac{3}{17} x+2[/tex]
The above equation would have a constant slope as it seems to be a linear function. ‘x’, the coefficient of the variable x is the slope of the function. Here,
[tex]x=\frac{3}{17}[/tex]
The rate of change of the function with respect to x referred as the slope of the function. Thus,
[tex]slope =\frac{\text { change of } f(x)}{\text { change of } x}[/tex]
[tex]\frac{\Delta f}{\Delta x}=\frac{3}{17}[/tex]
Given, x increases by 51. So, we have
[tex]\Delta x=51[/tex]
[tex]\frac{\Delta f}{51}=\frac{3}{17}[/tex]
Now solve for ΔF,
[tex]\Delta f=\frac{3}{17} \times 51=3 \times 3=9[/tex]
Thus, we have obtained that if x increases by 51, f (x) increases by 9.
