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(a) determine the domain, (b) sketch the graph and (c) determine the range of the function defined by the given equation.$f(x)=3 x-5$
(a) $-\infty<x<\infty$(b)(c) $-\infty<y<\infty$
Functions and their Applications
Basic Notions of Functions
Oregon State University
University of Michigan - Ann Arbor
Idaho State University
In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).
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So this problem We've been given the function f of X equals three X minus five. And there's three things we want to do for this. We're going to find the domain for this function, the range for this function, and then we're going to sketch it so we can see what it looks like. Okay, first, the domain. What are all of the possible values that we can put in? Remember, domains are X values. Well, often a good way to figure out the domain is to see if there's any values that you can't put in. And in this case, there is no limit. X could be anything I want. It could be positive. Negative zero A fraction, Um, square root. It doesn't matter all any number I want to pick. I can put into this function. So my domain is all real numbers. One way we often will identify. This is using interval notation, which means I'm going from I wanna have a parentheses there. From negative infinity to positive infinity. Okay. What about the range? Well, as ex gets bigger and bigger and bigger, so will the value of this function. As X gets more and more and more negative. So will this function. So my range is also all real numbers Negative. Infinity to infinity. Okay, So remember domain or my ex values range or my output or my y values. Now let's think about graphing this and I'm going to put in a Y instead of an f of X. Just I think this makes it a little bit easier to see. Why equals three X minus five. This is a line slope intercept form. So my slope is three or 3/1. And my Why intercept is negative five. So 1234 I could put negative five on my graph. And I have a slope of three up, 3/1 up, 3/1, and I just connect the dots. As you can see, our domain and range makes sense. We're just gonna go up without bounds on the one side, down without bounds on the other, every ex every yr possibilities in my domain and range. So this is domain range and sketch for my given function
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