{"id":7410,"date":"2016-07-26T09:47:40","date_gmt":"2016-07-26T16:47:40","guid":{"rendered":"https:\/\/magoosh.com\/sat\/?p=7410"},"modified":"2016-07-18T15:48:04","modified_gmt":"2016-07-18T22:48:04","slug":"sat-math-linear-functions","status":"publish","type":"post","link":"https:\/\/magoosh.com\/sat\/sat-math-linear-functions\/","title":{"rendered":"SAT Math: How to Solve Linear Functions"},"content":{"rendered":"

For linear functions, you will need to use your linear equation skills to solve problems the SAT throws at you. If you need a refresher on linear equations, check out our post on the Heart of Algebra section<\/a> on the SAT Math and head back here when you’re ready.<\/p>\n

\"New<\/p>\n

In the most basic terms possible, functions relate a set of inputs with a set of outputs. Usually, you will be able to spot a function when you see something like f(x) or g(x) instead of the usual y variable on one side of the equation.<\/p>\n

The key thing to remember about functions is that each input can only give you one output. For example, you can’t plug in 3 into a function and get two different answers. However, to different values of inputs can yield the same output.<\/p>\n

On a graph, an easy way to test whether or not a curve is a function is to use the vertical line test. If you draw an imaginary vertical line anywhere on the graph and it crosses the curve twice, then it is not a function. <\/p>\n

Most linear equations will pass the vertical line test. The only situation that you have to look out for is a line that is perfectly vertical. In that case, it is not a function.<\/p>\n

The standard notation for a linear function is f(x) = kx + f(0). <\/p>\n

The f(x) is similar to what the y-variable represents in a linear equation. Test makers can also call it the range or the output of the function.<\/p>\n

The k represents the slope. Take a moment to recall the slope-intercept form and note the similarities between the two.<\/p>\n

The f(0) is the y-intercept, or where the line passes through the y-axis when x=0.<\/p>\n

The x-variable can be called the domain or the input. The x-variable is what you can control, and the y is the value that you get based on what you put in. <\/p>\n

Don’t be overwhelmed by the verbiage. Just remember that you’re dealing with basically the same thing as a linear equation. The key here is to get used to all the terms that the test makers can throw at you.
\n <\/p>\n

SAT Math: Linear Function Graphs<\/h2>\n

Many problems you will encounter ask you to find a value of a certain coordinate point on a graph. In this case, f(x) corresponds to the y-axis and the x corresponds to the x-axis. <\/p>\n

All you have to do is go to a given spot on the curve see what the other coordinate equals. For example, if you see an ‘f(5)’, that means that you need to find what the y-coordinate is on the curve labeled \u201cf(x)\u201d where x = 5. <\/p>\n

SAT Math: Linear Function Tabular Notation<\/h2>\n

Sometimes, you will be given a chart of a function and be expected to interpret it. The chart will only give you a few values to work with. <\/p>\n

You will easily be able to see whether or not there is a linear relationship between the input and outputs. By comparing a few values, there should be a linear trend going upward or downward.<\/p>\n

The key here is to make sure that you keep your variables, inputs, and outputs straight. If you do that, you can handle any function table that comes your way. <\/p>\n","protected":false},"excerpt":{"rendered":"

For linear functions, you will need to use your linear equation skills to solve problems the new SAT throws at you. Develop those skills with this post.<\/p>\n","protected":false},"author":158,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[91],"tags":[],"ppma_author":[24918],"class_list":["post-7410","post","type-post","status-publish","format-standard","hentry","category-all"],"acf":[],"yoast_head":"\nNew SAT Math: How to Solve Linear Functions<\/title>\n<meta name=\"description\" content=\"For linear functions, you will need to use your linear equation skills to solve problems the new SAT throws at you. 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