Question

Help please
f(x)=2-sqrtx/2+3
What are my x and y intercepts and domain and range? I think I may have calculated something wrong :(

Answer 1

y intercept st x=0
x intercept set y=0 mean f(x)=0
and solve the equation
domain
is the function you wrote like this
\(\Large \bf\color{blueviolet}{f(x)=2-\sqrt{\frac{x}{2}+3}}\)

Answer 2

@Kerriy check the function
not sure what you wrote

Answer 3

Yes that is the function :)

Answer 4

Okay
for domain is any number x such that
\(\Large \sf\color{blueviolet}{\frac{x}{2}+3\geq0}\)
solve this inequality to get the domain

Answer 5

\[x \ge-6\]?

Answer 6

\(\large {
f(x)=2-\sqrt{\frac{x}{2}+3}
\\ \quad \\
\quad
\begin{cases}
y-intercept\to y=2-\sqrt{\frac{{\color{brown}{ 0}}}{2}+3}\to y=2-\sqrt{3}
\\ \quad \\
x-intercept\to {\color{brown}{ 0}}=2-\sqrt{\frac{x}{2}+3}\to \sqrt{\frac{x}{2}+3}=2
\\ \quad \\
\frac{x}{2}+3=2^2\to \frac{x}{2}=4-3\to x=2(4-3)
\end{cases}
}\)

Answer 7

y-intercept is easy just evaluate 0
\(\Large \sf\color{blueviolet}{f(0)=2-\sqrt{\frac{0}{2}+3}=2-\sqrt{3}}\)

Answer 8

Correct that's for domain
meaning all real numbers that greater than or equal to -6

Answer 9

You got the answer for everything!

Answer 10

what would my starting point be?

Answer 11

what do you mean by starting point?

Answer 12

no sorry my end point

Answer 13

end point for what, i don't get what you are trying to ask

Answer 14

Doesn't matter, I think I have worked it out.....thanks so very much for all your help :)

Answer 15

\(\Large \frak\color{blueviolet}{you~welcome}\)