Complete the table. g(x)=|2 x+3| x g(x) -3 -2 0 1

step 1 Here we have given here the function GX such that mode 2x plus 3. So as we know that a function

Complete the table. g(x)=|2 x+3| x g(x) -3 ...

Key Concepts

Absolute Value Function

The absolute value function, denoted by |x|, represents the non-negative value of x regardless of its sign. It is a fundamental concept in mathematics that is used to measure the distance of a number from zero on the real number line, and it transforms negative inputs into positive outputs while leaving positive inputs unchanged.

Function Evaluation

Evaluating a function involves substituting a given input value into the function's equation to calculate the corresponding output. This process is key in understanding how functions behave and how they transform inputs into outputs for various applications.

Linear Transformation

A linear transformation refers to a function that involves a linear expression, such as 2x + 3, which is then manipulated by additional operations like the absolute value. Understanding linear expressions and how they can be shifted or scaled is important for analyzing and graphing functions, especially when combined with other operations like the absolute value.

Transcript

00:01 Here we have given here the function gx such that mode 2x plus 3.

00:09 So as we know that a function is a rule that means if i have any number x then when we apply some rules on this number x we will find out a function called gx you can take any letter to represent a function fx g x and so on so i'm just representing the function by gx like this so so what is the gx a function that is a rule on any real number we can say that on or we can say that any number like x, then it will give the result of function g x.

00:41 And for an example, if i write here, g x is equal to x plus 3.

00:47 Okay.

00:48 So what is the rule here? just adding three in any number.

00:52 So if i have to find the value of g, we can say that the function at x is equal to 2, then when we, what we put we will put x is equal to 2 in this rule and find out the value of the function at x is equal to 2 that is 5 okay similarly we have to apply this concept on this function g x we have to fill the table here okay so in this table we okay i'm just writing it as g x okay so we have given here a table in which values of different values are given for x like minus 3 minus 2 minus 1 0 1 and 3 okay so now we have to find out the value of g x so we will apply the value of x on this rule to find out the value of function at x is equal to these values okay now first of all we will apply here x is equal to minus 3 so g minus 3 will be equal to here as more 2 into minus 3 plus 3 okay so as we know that this will give the result as minus 6 plus 3 so it will be equal to in mode minus 3 okay and after removing this mode it will be equal to 3 as you know that mode will give always positive result so g x will be equal to 3 for x is equal to minus 3 similarly when we put x is equal to minus 2 so the value of of function i'm just applying x is equal to minus 2 in this function so g minus 2 will be equal to here minus 4 plus 3 and that will give the result as after removing more 1 so minus 2 for x is equal to minus 2 the value of function g x is equal to 1 now coming to the next value that is minus 1 so the value of function g x at x is equal to minus 1 will be equal to minus 2 plus 3 and it will give the result as 1...

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