Question

HELP ASAP 29 POINTS A function, f, passes through the points (1,1), (2,7) and (3,25). A function, g, passes through the points (1,36), (2,43) and (3,50).
As the value of x increases, the values of f(x) and g(x) remain constant.



As the value of x increases, the value of f(x) will never exceed the value of g(x).



As the value of x increases, the value of f(x) will eventually exceed the value of g(x).



As the value of x increases, the value of f(x) and the value of g(x) both approach 100

Answer 1

Answer with explanation:

≡≡It is given that , function, f, passes through the points (1,1), (2,7) and (3,25).

Slope between two points is given by the formula

    $=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \text{Having coordinates} ,(x_{1},y_{1}),(x_{2},y_{2})$

→→You will find that,

       $\frac{7-1}{2-1}=6, \text{and} \frac{25-7}{3-2}=18 \text{and} \frac{25-1}{3-1}=12$

The slopes are not same.So, the given function is not linear.

Also, f(1)=1, f(2)=7,f(3)=25

1+6=7+18=25,f(x) increases each time  differently ,first by a number of ,6 ,then by 18,may be then by 54,....with increase in value of x , by 1 unit.

≡≡The function, g, passes through the points (1,36), (2,43) and (3,50).

    Slope between two points is

  $\frac{43-36}{2-1}=\frac{50-43}{3-2}=\frac{50-36}{3-1}=7$

36 +7=43+7=50+7=57

So,the function is linear.

f(x) increases each time with same digit,that is by value of 7, with increase in value of x , by 1 unit.

Option C:⇒As the value of x increases, the value of f(x) will eventually exceed the value of g(x).

       

Answer 2

As the value of x increases, the value of f(x) will never exceed the value of g(x).