hooglswiss.blogg.se - Sketching functions worksheet

This gives us the function $y=\frac52x+5$.

The rise of the right line is $5$ and the run is $2$.

So the corresponding function is $y=-\frac52x+5$.

You get the slope using "rise over run": for the left line we have a rise of $-5$ and a run of $2$.

The line on the lieft has a negative slope while the line on the right has a positive slope.

But what is the difference? It's the slope!

The line on the left has the y-intercept $5$ as well as this one on the right.

A parabola corresponds to a quadratic function.

A line corresponds to a linear function.

Here you have two lines and two parabolas. Holy moly! Stop the presses! What's that? She thinks she's finally discovered a new celestial body. Is it a function? It fails the test, so no way. Whoa nelly! This one looks like a circle. For each input, there is more than one output. It fails the vertical line test, so no, it’s not a function. Here’s another awesome constellation, but does its graph form a function? Because the graph passes the vertical line test, it sure does!Īnd, what about this one? It’s u-shaped, but it’s turned sideways. Oh look! It passes the test! So this graph is also a function - for each input, 'x', there is one output, 'y'. It’s so curvy is it a function? Let’s use the vertical line test to see if it is. Looking through her telescope, Stephanie sees a constellation. How do we know if a quadratic equation is a function? For each x, there is only one y, and the graph passes the vertical line test. When you have a quadratic equation, the graph is always a parabola. This distinctive u-shape is called a parabola. To do this, we can create a function table and calculate a few points, then graph. If any line touches the graph in more than one place, it's not a function - it's that simple! Graphing Parabolas Draw in several vertical lines, if the lines touch the graph in only one place, then the graph is a function. To double check that the graph is a function, we can also do a vertical line test. We know the graph displays a function because each 'x' has only one 'y'. Next, plot a few points and connect the points on the line.

OR, you can write the values for 'x' and 'y' in a table. The y-intercept is equal to 8, and the slope, or rise over run, is equal to 2. It’s already written in slope-intercept form, y = mx + b. Notice that we used the function notation, f(x), this is just a fancy way of representing 'y'. Let’s take a look at the function f(x) = 2x + 8. If the graph of the star's path is a function, then for every input, time, there is a unique output, the location or the distance traveled. For each minute that passes, the star travels to a new location in the sky. To show the relationship between distance and time, we can look at a graph the path of the star MAY be the graph of a function, but how do we know for sure?Ī function is a special relationship between two variables in this case, the variables are the distance and the time.

Although she knows the average speed of a shooting star is 30,000 miles per hour, she wonders about its path and how far it'll travel in a given amount of time. She sees a shooting star - which is a small, fast meteor. From her backyard, she gazes through her telescope and dreams of discovering a new celestial body.

Stephanie Gawking is a math enthusiast, and her hobby is astronomy. Otherwise, the graph does not represent a function.Īnalyze functions using different representations. To determine if the graph is a function or not, we use the vertical line test: if any vertical line touches only one point of the graph, then the graph represents a function this means graphically that every x is assigned to exactly one y. the y values) gives the horizontal projection of the graph. the x values) gives the vertical projection of the graph, whereas the range (i.e. (4) If the equation is linear, connect the points with a line, otherwise connect the points with a smooth curve. (3) Plot the resulting ordered pairs (x,y) in the plane. (2) Substitute in each value of x into f(x) the result will be the y value of the x which was plugged in.

To graph a function f(x), follow the following steps: Graphing functions is pretty much the same as graphing equations, with the symbol f(x) being a fancy way of writing y.