Question

Please determine the x and y intercepts algebraically image attached much appreciated

Answer 1

To determine the y intercept of a function we need to remember that it happens when x=0; plugging this value in the expression for the function we have:

`\begin{gathered} f(0)=\log_(2-0)√(0+3) \\ f(0)=√(3)\log2 \end{gathered}`

Therefore, the y-intercept is

`(0,√(3)\log2)`

To determine the x intercept we need to remember that this happens when the value of the function is zero, then we equate the expression to zero and solve for x:

`\log(2-x)√(x+3)=0`

Now, we know that a product is zero only if one of the factors is zero, then this equation leads to the following two equations:

`\begin{gathered} \log(2-x)=0 \\ √(x+3)=0 \end{gathered}`

Solving the first one we have:

`\begin{gathered} \log(2-x)=0 \\ 2-x=10^0 \\ 2-x=1 \\ x=2-1 \\ x=1 \end{gathered}`

Solving the second equation we have:

`\begin{gathered} √(x+3)=0 \\ x+3=0 \\ x=-3 \end{gathered}`

Therefore, the x-intercepts are (-3,0) and (1,0)