Question

Okay, so I have a question about a problem on my homework for math. The instruction only tell me to Identify the domain, range, y-intercept and x-intercept(s). I have no idea what to do at all because I only thought you could find the domain and range for functions. The equation I need to find this is f(x)=x^2 - 2x - 3. I am so confused, so explain this step by step thanks!

Answer 1

the domain of a function is the input values. Meaning, what can x be?
well, x can be any value. Meaning, if you put x in the function the function is always defined. So the domain of the function is the set of real numbers
The range of a function is the output values. What can f(x) be?
f(x) can also be any value. For every f(x) value there is an x that satisfies
f(x)=x^2 - 2x - 3
The Y-intercept is where the graph of the function intersects the y-axis.
So you set the x-value in the function to zero and have. f(0)=0^2-2(0)-3=-3
The x-intercept is where the graph of the function intersects the x-axis.
Now solve x^2-2x-3=0

Answer 2

domain is any x number, or more formally [ - \[\infty, \infty\] ]
The range is found by taking the first derivative, which you definitely don't know about. The alternative is looking at the graph. See how it goes down forever and up forever? The range is the same as the domain. to find the y intercept find what it is when x=0, so f(x)=0-0-3=-3. To find the x intercept find what x is when y = 0, and to do this you plug x^2-2x-3=0 into the quadratic formula. X is equal to \[(-b \pm\sqrt{b^2-4ac})/2a\], with a=1, b=-2, and c=-3 (from the original formula, ax^2+bx+c). This will give you two answers

Answer 3

Thank you for that great answer! You helped me a lot!
Both of you ,so you both get a medal !!!