1. ## Precalculus Problem

Any help would really be appreciated:

Express the distance from point (x,y) on the graph y = 4 - x^2 to the point (0,1) as a function of x. Give the domain of the function.

2. compute the difference quotient for (f(x+h) - f(x))/h for f(x) = 3x + 8, and f(x) = 1/x^2

2. Originally Posted by skabani
Any help would really be appreciated:

Express the distance from point (x,y) on the graph y = 4 - x^2 to the point (0,1) as a function of x. Give the domain of the function.
The distance formula says the distance, $d(x,y)$, between two points $(x_1, y_1)$ and $(x_2,y_2)$ is given by:

$d(x,y) = \sqrt {(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Hint:

For the graph $y = 4 - x^2$, any arbitrary point $(x,y)$ on the graph can be represented as $\left( x,4 - x^2 \right)$

3. so would the answer be the square root of x^4 -7x^2 - 2x + 15 ??

4. Originally Posted by skabani
so would the answer be the square root of x^4 -7x^2 - 2x + 15 ??
no. look at the formula again. there should be no x's in your answer, the lowest power of x would be 2 when you square the things in the brackets

5. so then would it be the square root x^4 - 7x^2 + 9?

and could you help me with the function problems too..

for the first one, f(x) = -3x + 8, i got 1
and for the second one, f(x) = 1/x^2, i got (-2x-h)/[(x^2)(x+h)^2]

thanks for all ur help!!