Hi everyone, welcome to the review session for this unit. In this unit you've learned how to determine a function, and how to recognize it from its graph. You can also describe the behavior of a function. Find the maximum and minimum, and determine if it's even or odd. Let's check your understanding with a few problems.
Since we've helped Athena come to an understanding of what a function is, we are going to begin the review of functions with the equation y equals x squared minus 1. First, we want you to think about how you would determine whether or not this is a function. So consider that for a second, and type what you think you should do to figure this out in this box.
So using what you just thought about, is this a function? Please answer yes or no.
We would need to make sure that each element of the domain is paired with exactly one element of the range of the function. One way to do this graphically would be to draw the curve, and then, to use the vertical line test to see how many places this curve touches any given vertical line. If it never touches any vertical line more than once, then it is a function. And it looks like the answer in this case is, yes, this is a function.
Let's look at this problem a little deeper. Can you find the domain and range of the function? Please write your answers in interval notation.
If you answered all real numbers for the domain, you're correct. And the range is negative 1 to infinity.
Finally is the function even, odd or neither, and how do you know this?
As you may have noticed from the graph, this graph is symmetric about the y-axis, and is therefore an even function. As a review, if the function was symmetric about the origin, it would be an odd function. An example of an odd function would be f of x equals x cubed. Here is what the graph looks like. This graph is symmetric about the origin.
Let's take a look at another function - f(x) = x³ - 5x Please find the following information about the function: What is the domain? The range? Is the function even or odd? And describe the function behaviour.
Here is six graphs, please match each graph with the equation below.
And the solutions are, f of x equals 2 x plus 3 corresponds with letter c. F of x equals x squared plus 6 corresponds with graph of the letter b. F of x equals and f of x equals the absolute value of x minus 2 corresponds with letter d. And finally, f of x equals the square root of 3x plus 2 corresponds with letter e.
Take a look at each of these functions. Please write in the domain and range of each function using inequality notation. As well include whether or not the function is even, odd or neither.
So let's look at our first function, f of x equals 2x plus 3. The domain is all real numbers, as is the range. And, this function is neither even nor odd. Let's look at our second function, f of x equals x squared plus 6. Our domain is again all real numbers. Our range is y greater than or equal to 6. And this is an even function. Lets look at f of x equals negative 2. Our domain is again all real numbers, but our range is restricted to y is equal to negative 2. And this is an even function. Lets look at f of x equals x cubed minus 1. The domain is all real numbers, as is the range, and this is neither even nor odd. Let's look at the function f of x equals the absolute value of x minus 2. The domain is all real numbers. The range is y is greater than or equal to 0. And this is neither even nor an odd function. Our last function, f of x equals the square root of 3 x plus 2. Our domain is x is greater than or equal to 2 3rds. Our range, y greater than or equal to 0. And again, this is neither even nor an odd function.