Tell whether the function is linear. Then evaluate the function for the given value of x.



6.) f(x)= 3-3x; f(2)

7.) f(x)= | x+2 | ; f(-4)

8.) f(x)= 2/x-2; f(6)

14.) f(x)=2/3x-5 ; f(9)

Can someone help me with these^^. please write the QUESTION # SO I know which one the answer refers to. Merci.

Sure! I will answer each question one by one.

Question 6: To determine whether the function f(x)=3-3x is linear, we need to check if the degree of x is 1 and there are no other variables or operations involved. Here, the degree of x is 1, and we only have multiplication and subtraction operations, so the function is linear.

To evaluate f(x) for f(2), we substitute x=2 into the function:
f(2) = 3 - 3(2) = 3 - 6 = -3

Therefore, f(2)=-3.

Question 7: The function f(x) = |x+2| is not linear because it involves the absolute value function, which introduces a non-linear element.

To evaluate f(x) for f(-4), we substitute x=-4 into the function:
f(-4) = |-4+2| = |-2| = 2

Therefore, f(-4)=2.

Question 8: The function f(x) = 2/(x-2) is not linear because it involves division, which introduces a non-linear element.

To evaluate f(x) for f(6), we substitute x=6 into the function:
f(6) = 2/(6-2) = 2/4 = 1/2

Therefore, f(6)=1/2.

Question 14: The function f(x) = 2/(3x-5) is not linear because it involves division, which introduces a non-linear element.

To evaluate f(x) for f(9), we substitute x=9 into the function:
f(9) = 2/(3(9)-5) = 2/(27-5) = 2/22 = 1/11

Therefore, f(9)=1/11.

I hope this helps! Let me know if you have any further questions.

Of course! I can help you with these questions. Let's go through each one and determine whether the function is linear and then evaluate it for the given value of x.

6.) f(x) = 3 - 3x; f(2)
To determine whether the function is linear, notice that the function is in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, m = -3 and b = 3. Since the function is in the form of a linear equation, we can conclude that the function is linear.

To evaluate the function for the given value of x, substitute x = 2 into the function:
f(2) = 3 - 3(2)
f(2) = 3 - 6
f(2) = -3

So, f(2) = -3.

7.) f(x) = |x+2|; f(-4)
To determine whether the function is linear, notice that the function involves an absolute value operation. Linear functions do not involve absolute values. Therefore, the function is not linear.

To evaluate the function for the given value of x, substitute x = -4 into the function:
f(-4) = |-4 + 2|
f(-4) = | -2 |
f(-4) = 2

So, f(-4) = 2.

8.) f(x) = 2/(x-2); f(6)
To determine whether the function is linear, notice that the function includes a fraction with x in the denominator. Linear functions do not have denominators with x in them. Therefore, the function is not linear.

To evaluate the function for the given value of x, substitute x = 6 into the function:
f(6) = 2/(6-2)
f(6) = 2/4
f(6) = 1/2 or 0.5

So, f(6) = 0.5.

14.) f(x) = 2/(3x-5); f(9)
Similar to the previous question, this function contains a fraction with x in the denominator. Therefore, it is not a linear function.

To evaluate the function for the given value of x, substitute x = 9 into the function:
f(9) = 2/(3*9-5)
f(9) = 2/(27-5)
f(9) = 2/22
f(9) = 1/11 or approximately 0.0909

So, f(9) ≈ 0.0909.

I hope this helps! If you have any more questions, feel free to ask.

6, linear, 3 -6 = -3

7, V shaped, not linear -4+2 = -2 but |-2| = +2

8, certainly not linear, infinite (undefined) at x = 2 !!! You had to ask me that ????
2 /(6-2) = 1/2

14, same sort of problem as 8