Graph each function. ƒ(x) = {|x| if x

Question

Graph each function. ƒ(x) = {|x| if x < 3 , 6-x if x ≥ 3}

Piecewise function definition for f(x) with conditions for x values.

Accepted Answer

Graph. The following equation F of X equals the absolute value of four, X. If X is less than four and negative X plus 20. If X is greater than, or equals to four, we have a few assorted graphs here to determine the graph. Let's test a few points and see if any of them line up with our possible graphs. Let's say we take F of negative five first and A, the five is in the domain X is less than four. So we would use our absolute value equation that the value of four multiplied by 90 to 5 S equal slaps the value of negative 20 for instance, which just gives us 20 meaning we have a point at negative 20. Let's take another point. Let's say we have F of zero, absolute value four multiplied by zero, gives us the absolute value of zero, which is just zero via the point also at 00. Test another point. Let's say we used that before which F of four happens on our second equation negative X plus 20 based on our greater than or equal to sign, we get negative the four plus 20 which is equals to 16. We then have a point at 4 16. Finally, we'll check one more point. Let's check 20. For instance, F for 20 gives us negative 20 plus which is zero, giving us a point at 20 0. Now, we can find the graph that has all four of these points. If we look over, we can determine graph A actually has every point that we found. OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Graph each function. ƒ(x) = {|x| if x < 3 , 6-x if x ≥ 3}

Key Concepts

Piecewise Functions

Absolute Value

Graphing Techniques

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