so this is evaluating functions and "evaluate the function when x = 2, x = 0 and x = -2
1. f(x) = 3x
2. g(x) = -x - 6
3. h (x) = 8x + 7
what do the variables at the beginning of the equation mean? (the f , g and the h) thanks :)
f(x) = y
g(x) = y
h(x) = y
whenever you see: "letter(letter)", you know it is y. And y is the y value on the Cartesian coordinate plane. Evaluating the function means solve for y, so just plug in the numbers you are given into x (aka substitution) and your "y" value is your answer.
so can you solve one of the problems for me as an example because I don't really understand what you're saying?
1.
Question: f(x) = 3x
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Step 1:
State the given.
You are given x=2, x=0, and x=-2.
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Step 2:
Plug in(A.K.A. "substitute) the numbers.
Plug in 2 for x in "3x". Plug in 0 for x in "3x". Plug in -2 for x in "3x". THESE ARE THREE DIFFERENT EQUATIONS NOW, DON'T GET THEM CONFUSED!
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Step 3:
Solve.
3 * 2 = 6
3 * 0 = 0
3 * -2 = -6
(2, 6) | (0, 0) | (-2, -6) are your data points.
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Now try and do the same thing for the other two problems
The variables at the beginning of the equations, namely f, g, and h, are known as function names or function symbols. They are used to represent different functions or mathematical operations. Each function can be thought of as a specific rule or set of instructions for manipulating the input values (in this case, x) to produce corresponding output values.
In the given equations, we have three different functions: f(x), g(x), and h(x). To evaluate each function at specific values of x, we simply substitute those values into the equation and calculate the resulting output value.
Now, let's evaluate each function when x takes on the values of 2, 0, and -2:
1. For f(x) = 3x:
- When x = 2: f(2) = 3 * 2 = 6
- When x = 0: f(0) = 3 * 0 = 0
- When x = -2: f(-2) = 3 * (-2) = -6
2. For g(x) = -x - 6:
- When x = 2: g(2) = -(2) - 6 = -8
- When x = 0: g(0) = -(0) - 6 = -6
- When x = -2: g(-2) = -(-2) - 6 = -4
3. For h(x) = 8x + 7:
- When x = 2: h(2) = 8 * 2 + 7 = 16 + 7 = 23
- When x = 0: h(0) = 8 * 0 + 7 = 0 + 7 = 7
- When x = -2: h(-2) = 8 * (-2) + 7 = -16 + 7 = -9
So, the values obtained by evaluating the functions for x = 2, x = 0, and x = -2 are as follows:
1. f(x): f(2) = 6, f(0) = 0, f(-2) = -6
2. g(x): g(2) = -8, g(0) = -6, g(-2) = -4
3. h(x): h(2) = 23, h(0) = 7, h(-2) = -9