Hello wonderful mathematics people, this is Anna Cox from Kellogg Community College here are nine of the basic graph types. f(x) is the square root of x: the domain includes zero and goes out to infinity. The range includes zero and goes out to infinity. Here's a rough sketch of what it looks like it's neither even or odd because it's not symmetrical around the origin for the y-axis if we look at f(x) equal the cube root of x, the domain is all real numbers with is written as negative infinity to infinity. The range is negative infinity to infinity. It is an odd function because the y-value at negative x equals the opposite of the y-value at x. Here's another sketch of that graph f(x) equals the absolute value of x: the domain is all real values. The range is only the positives and zero it's an even function because it's symmetric around the y-axis, i.e. the y-value at negative x is the same thing as the y-value at x if we look at the constant function, f(x) equals b, the domain is all reals. The range is just the value for b, because no matter what we put in, we're only getting be out it is an even function because the y-value at x is equivalent to the y-value at negative x. Here is a graph Um, this is assuming b is whatever that value up is f(x) equals x is called the identity function. The domain is all reals, the range is also all reals. It is an odd function because the y-value at negative x equals the opposite of the y-value at x. Here's a graph f(x) equal x squared. Domain is all reals, the range is zero to infinity including zero it's an even function, it's a graph of a parabola and the y-value at x equals the y-value at negative x f(x) equal x cubed the domain is all reals. The range is all reals. It's an odd function i.e. the y-value at negative x equals the opposite value of the y-value at x. Here's a rough sketch f(x) equals one over x, sometimes referred to as a reciprocal function the domain is negative infinity to zero union zero to infinity it can't include zero because we don't know how to divide by zero. One divided by zero is undefined the range is actually the same thing. Negative infinity to zero not including zero union zero to infinity it's an odd function so f(-x) equals the opposite of f(x). Here's a rough graph of what it would look like the last one is a linear function f(x) equals mx plus b. b is the y-intercept. It's actually a point zero b, y-intercept and the m is the slope in the picture to the right I have a slope that is positive and b intercept anywhere we want to have it. Domain is negative infinity to infinity. Range also negative infinity to infinity the function might be odd if b equal zero. If b doesn't equal zero, then it's not even or odd thank you and have a wonderful day