f(x)=3x^2-x-2
If x=2, what is f(x)? What point is on the graph of f?
For the first question, I got 8. But, I'm having trouble understanding the second question.
To find the value of f(x) when x=2, you can substitute x=2 into the given function f(x)=3x^2-x-2.
f(x) = 3(2)^2 - 2 - 2
= 3(4) - 2 - 2
= 12 - 2 - 2
= 8
So, when x=2, f(x) equals 8.
Now let's address the second question. "What point is on the graph of f?"
The graph of f(x) represents the relationship between the x-values and their corresponding y-values. In this case, the graph of f(x)=3x^2-x-2 is a parabolic curve.
To find a specific point on the graph, we need to know both the x-value and its corresponding y-value. In this case, we know that when x=2, f(x)=8.
Hence, the point on the graph of f is (2, 8). This means that when x=2, the y-coordinate or the output of the function f(x) is 8.
To find the value of f(x) when x=2 in the equation f(x)=3x^2-x-2, we can substitute the value of x into the equation and evaluate it.
So, plugging in x=2 into the equation f(x)=3x^2-x-2:
f(2) = 3(2)^2 - 2 - 2
= 3(4) - 2 - 2
= 12 - 2 - 2
= 8
Therefore, when x=2, the value of f(x) is 8.
Now, let's move on to the second question: "What point is on the graph of f?"
The graph of a function represents its output values (y or f(x)) for different input values (x). In this case, the function f(x)=3x^2-x-2 represents a parabola because it is a quadratic function.
To find a point on the graph of f, we can choose a specific value for x and calculate the corresponding value of f(x).
For example, let's find the point on the graph of f when x=2. We have already found that f(2) = 8, so the point on the graph of f when x=2 is (2, 8).
In coordinate form, the point on the graph of f is (x, f(x)), so when x=2, the point on the graph is (2, 8).
f(x) and y are interchangable
so instead of
f(x) = 3x^2 - x - 2 you can say
y = 3x^2 - x - 2
so when x = 2 , y = 12 - 2 -2 = 8 which you had
so you are dealing with the point (2, 8)
the x is 2, the y is 8