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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.$f(x)=4 x+1$

(a) $-\infty<x<\infty$(b)(c) $-\infty<y<\infty$

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

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Harvey Mudd College

Lectures

01:43

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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(a) determine the domain, …

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(a) draw the graph of the …

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for this problem. We've been given a function f of X equals four X plus one. We want to find both the domain and the range for this function. And then we're going to sketch the function on the grid. So domain and range, remember, domain are my inputs, those air, my ex values range is my out put Those are the values that I get when I put in my exes So range you could think of those as your y values. So when we want to know what possible values of X can go into my domain, it's often useful to think of it in reverse. What exes cannot be put into my function. And in this case, there are no exes that are excluded. X could be positive. Negative zero a fraction a million. Any ex you come up with can get put into this function. So my domain is all real numbers One way we often right. This is an interval notation, which means X is going to go from negative infinity to positive infinity. And what about range? Well, as X becomes a very, very large positive number, so will my function as X becomes a very, very, very large negative number. So does the output of the function. So my range is also all real numbers. Negative. Infinity to positive infinity. So let's sketch this and you can see the domain and range for yourself. I'm going to rewrite this, but I'm gonna use why? Because we're used to using why, instead of ffx when we go to sketch things. So why equals four X plus? What? Well, this is a line in slope intercept form. So my slope is four and my Why intercept is one I want to go to graph that there's my white intercept. My slope is 4123 up, four over. One up, 4/1. And I'm just gonna connect these dots. As you can see, I'm going to be going up. X and Y are both could be increasing without bounds. I go up toward the write off of off of the grid here, and as X becomes more and more negative, so does why every single X and Y is possible to be within my domain and my range. So domain and range, plus my sketch for the given function

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