Question

Exercises Complete the following: 11. Find the intercepts and (a) 9x² - 164 = 144 (c) 25x - 4y = 100 (e) x² + y² = 1 29x² + 16y² = 144

Answer 1

`-x^2+y^2=1`

The intercepts for a function can be on either of the two axis, y or x.

when finding the intercepts of x, means that y = 0

when finding the intercepts of y, means that x = 0

finding the x intercepts

`\begin{gathered} -x^2+(0)^2=1 \\ -x^2=1 \\ x^2=-1 \\ x=\sqrt[]{-1} \end{gathered}`

since the solution for the square root of -1 has not any solution on the real numbers, we can say that there is no intercept over the x axis.

finding the y intercepts

`\begin{gathered} -(0)^2+y^2=1 \\ y^2=1 \\ y=\pm\sqrt[]{1} \\ y=1;y=-1 \end{gathered}`

there are 2 intercepts on the y axis, these are at y=1 and y=-1

information can be proven by graphing the function