# Given the graph of a function f(x) explain how to find (i) f(a) for a given value of a (ii) domain range of f(x) (iii) x-y-intercepts of f(x).Demonstrate (i)(i)(iii) by providing an example

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### 1 Answer

Let's just take the example `y=1/(x-2)^2+1`

1. To find the value of the function for a given x value, you substitute into the function and evaluate. For example, let x = -1. Then `f(-1)=1/(-1-2)^2-1=1/(-3)^2-1=1/9-1=-8/9`

2. Domain is all allowable x-values for the function. In our function, we have a fraction, so we should be wary of dividing by 0. What x-value would make the denominator 0? x=2. So Domain here is all real numbers except 2.

Similarly, range is all possible output values of the function. Take a look at the graph. Since the graph of the function never reaches -1, the range of the function is all real numbers greater than -1.

3. The y-intercept is pretty straightforward. Plug in x=0 and you'll find where the function crosses the y-axis (if it does). Here, f(0) = 1/(0-2)^2-1 = 1/4-1 = -3/4.

Finding x-intercepts is just the opposite. Let f(x) = 0 and solve for x. Here we end up with two x-intercepts:

`0=1/(x-2)^2-1`

`1=1/(x-2)^2`

`1=(x-2)^2`

`+-1=x-2`

`x = 3, 1`