Find the function values. g(x)=2 x+3 a) g(0) b) g(-4) c) g(-7) d) g(8) e) g(a+2) f) g(a)+2

Name: Problem 53, Chapter 3: Elementary and Intermediate Algebra
Uploaded: 2020-06-20T05:12:54-08:00
Duration: 5 min 18 s
Channel: Kelsey Dondelinger
Description: Find the function values. g(x)=2 x+3 a) g(0) b) g(-4) c) g(-7) d) g(8) e) g(a+2) f) g(a)+2

Find the function values. g(x)=2 x+3 a) g(0) b) g(-4) c)...

Key Concepts

Substitution in Algebraic Expressions

Substitution is the process of replacing a variable in an expression or equation with a given value or another expression. This concept is crucial when evaluating functions because it allows one to transform abstract expressions into concrete numerical results, or to maintain a degree of generality by substituting expressions containing parameters.

Function Evaluation

Function evaluation involves determining the output of a function by substituting a specific value for the input variable into the function’s expression. This process is fundamental in understanding how functions assign outputs to inputs and is essential for solving problems in algebra and calculus.

Linear Functions

A linear function is a type of function that can be expressed in the form f(x) = mx + b, where m represents the slope of the line and b represents the y-intercept. Linear functions are characterized by their constant rate of change, and they produce straight-line graphs, making them one of the most basic and widely used classes of functions in mathematics.

Transcript

00:01 So this is a problem that gives us a function, and we're asked to evaluate the function in a variety of different x values or input values.

00:07 So for example, if our function was g of x equals 2x plus 3, if we're given specific x values or input values, we can substitute those for x in our function to determine its output value or its y value.

00:25 So for example, a function notation, if i wanted to evaluate the function g, that means i'm going to use this function that i've been given, i can be given a specific input or x value.

00:36 So let's say that input was zero.

00:39 That means in my function, 2x plus 3, the x value or the input that they would like to evaluate is when the input is 0.

00:47 So i'm going to replace the x value with 0 and leave everything else the same.

00:53 So instead of 2x plus 3, we now have 2 times 0 plus 3, because 0 is the input i was given to evaluate.

01:00 And then if we work out that algebra, we have 2 times 0, which is 0.

01:05 Plus 3, which just equals 3.

01:09 So therefore, g of 0 equals 3.

01:17 Looking at a different example, we had g of negative 4.

01:23 Again, we do the same thing.

01:25 So we're going to replace, we're going to keep the 2 in the function.

01:28 We're going to replace this x value with the input we've been given, which is negative 4.

01:34 Working that out, 2 times negative 4 is negative 8, plus 3 more gives us negative 5.

01:42 So g, the function g, when the input is negative 4, gives us an output of negative 5.

01:51 And we can continue this process with any input that's been given to us.

01:55 So it could be a number, it could be a letter, it could be an expression.

01:59 So continuing through, let's look at g of negative 7.

02:05 We're going to use our expression, 2 times negative 7 plus 3.

02:10 2 times negative 7 is negative 14, plus 3 more is negative 11.

02:16 So g of negative 7 equals negative 11...

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