# Slope-intercept, (determine, evaluate, domain) function, diff. quotient

• Eshmael
Do you want to see me do the other ones?In summary, the conversation revolves around determining the domains of three given functions. The main concern is understanding how to evaluate the functions and identify any restrictions, such as not being able to divide by 0 or take the square root of a negative number. The domain for the first function is all real numbers, for the second function it is all positive real numbers, and for the third function it is all positive numbers excluding 0.
Eshmael
Domain Functions:

f(x) = 4sq.root(1-x2), the 4 is on the outside

f(s) = sq.root(s -1)/s-4

f(x) = x-4/sq.root x

I have absolutely no clue how to go about doing any of these, I take notes but I cannot piece it together; I have never felt so helpless at anything. This isn't homework I just want to know how to be able to do slope-intercept, determine a function, evaluate it, domain functions and difference quotients becaue I have a quiz on it tomorrow at 8:30 and I need to know how to at least start to solve them.

You asked for the domains of these functions according to what you expressed in pure text form:

f(x) = 4$$\sqrt{1-2x}$$

f(x) = $$\frac{\sqrt{s - 1}}{s}$$ - 4

f(x) = x -$$\frac{4}{\sqrt{x}}$$

Are those the functions you meant?

symbolipoint said:
You asked for the domains of these functions according to what you expressed in pure text form:

f(x) = 4$$\sqrt{1-2x}$$

f(x) = $$\frac{\sqrt{s - 1}}{s}$$ - 4

f(x) = x -$$\frac{4}{\sqrt{x}}$$

Are those the functions you meant?

Yeah, if you could just like direct to a website which explains these as a lesson or something, that would be great.

The "domain" of a function, if nothing but the formula is given, is all values of x for which the formula can be evaluated. For most functions the only problems are:
1) You can't divide by 0
2) You can't take the square root of a negative number.

Look at the last one:
$$f(x)= x- \frac{4}{\sqrt{x}}$$
That first x is no problem- you could replace it with any number. But the other x is inside a square root- it can't be negative. Also it is in the denominator: $\sqrt{0}$ certainly exists, it is 0. But then you would be dividing by 0 so x also cannot be 0. In stating what the domain is you would reverse that: x cannot be negative or 0 so x can be any positive number. The domain is the set of all positive real numbers.

## What is slope-intercept form?

Slope-intercept form is a way to represent a linear function using the equation y = mx + b, where m is the slope of the line and b is the y-intercept, or the point where the line crosses the y-axis.

## How do you determine the slope of a line using slope-intercept form?

To determine the slope of a line using slope-intercept form, you can simply look at the coefficient of the variable x. This coefficient, or number in front of x, represents the slope of the line.

## What does it mean to evaluate a function?

Evaluating a function means to plug in a given value for the independent variable, or x, and solve for the corresponding output, or y. In other words, you are finding the value of the function at a specific point on the graph.

## What is the domain of a function?

The domain of a function is the set of all possible input values, or x-values, for which the function is defined. In other words, it is the set of values that can be plugged into the function to get a valid output.

## What is the difference quotient?

The difference quotient is a formula used to find the average rate of change of a function over a specific interval. It is written as [f(x+h) - f(x)] / h, where h represents the change in the input value (or x) and f(x) represents the function itself.

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