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Question 891575: Tell whether the function is linear. Then evaluate the function for the given value of x. The function is f(x) = x + 5; f(-2)
My work:
-2x = x + 5
-1x -1x
-3x = 5
-3x/-3 = 5/-3
x = -5/3
However, I'm not sure if I solved that correctly, and I don't know how to fid out if its a linear or not. Thanks for your help!!!
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Given;
(1) f(x) = x + 5
This is linear because the variable, x, occurs in the function (named f) to the first power. If you had x^2, it would not be linear. Another view of linear is that the function is a straight line. In this case the line has a slope of 1 and the intercept of 5. Think of letting y = f(x), then you have the familiar equation of a straight line in the slope/intercept form, or y = x + 5. In algebra, linear means a straight line.
To evaluate a function at a particular value of the argument, x in this case, simply substitute that value for x where ever it appears in the definition of the function.
In this case we want f(x) as given in (1), when x = -2, or
(2) f(-2) = (-2) + 5 or
(3) f(-2) = 3
See where you went wrong?
If you wanted f(17), you have
(4) f(17) = 17 + 5 or
(5) f(17) = 22
Get it?
PS A function does not have to be linear to get its value at a certain argument. By the way, the argument is anything within the parentheses of the function's name. For example we could for the function in (1) get
(6) f(c-3) = (c-3) + 5 or
(7) f(c-3) = c +2
If we had the (non-linear) function
(8) g(x) = (x^3 - 2x^2)/3
We get
(9) g(-1) = ((-1)^3 - 2(-1)^2)/7 or
(10) g(-1) = (-1 - 2)/3 or
(11) g(-1) = -1
Hope this helps, you'll use functions a lot in your future.
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