the piecewise function h(x) is shown on the graph. what is the value of h(3)? –2 –1 1 2 This is a topic that many people are looking for. savegooglewave.com is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, savegooglewave.com would like to introduce to you Evaluating Piecewise Functions. Following along are instructions in the video below:
This lesson. Were gonna focus on evaluating piecewise functions a piecewise function is a a function that can be broken up into many parts so this particular piecewise function be equal to 4x plus. 5.
Or 3x minus 8 depending on the x value so lets say its equal to 4x plus. 5. When x is less than 2 and is equal to 3x minus 8.
When x is equal to or greater than 2. So go ahead and find the value of f of negative 2 f. Of 2 and f of 5 feel free to pause the video and work on his problem.
So lets evaluate the function when x is negative. 2. So should we use this portion of the piecewise function or the bottom part should we use 4x plus 5 or 3x minus 8 negative.
2 is less than positive. 2. Its not equal to or greater than positive 2.
So therefore negative 2 corresponds to this range. So we need to use the first part of the piecewise function. So lets replace x with negative 2 4 times negative 2 is negative 8 negative 8 plus 5 is negative 3 so f of negative 2 is negative 3.
Now what about f of positive. 2. Should we use 4x plus.
5. Over 3x minus.
8. Now x is equal to 2. And this equality.
Not in this one. So we have to use 2x minus. 8.
So its going to be. 3. Times.
2. Minus. 8.
3. Times. 2.
Is 6 6. Minus. 8.
Is negative. 2. And thats the answer now.
What is the function value at 5. So once again.
5. Is greater than 2 so we need to use 3x minus. 8.
So its gonna be 3. Times. 5.
Minus 8 3. Times. 5.
Is 15 15 minus. 8. Is 7.
And thats it lets work on some more examples so lets say if we have the function f of x. And its equal to x. Squared.
Plus 3x minus 7. When x is less than negative. 1.
And its equal to 5x plus. 6. When x is greater than or equal to negative.
1. Actually let me change that lets say when x is greater than or equal to negative 1.
But less than 2 and lets say its equal to x. Cubed plus. 4.
When x is greater than 2. And is equal to 12. When x equals.
2. So with this information. I want you to evaluate f of negative.
4 f. Of lets say 0 f. Of 2 and f of 3.
So feel free to pause. The video and try that so lets evaluate the function at x equals 2 negative 4 so negative. 4 is less than negative 1 therefore we need to use x squared plus 3x minus 7.
So this is gonna be negative. 4 squared plus 3 times negative 4 minus 7 negative 4 squared or negative 4 times negative. 4 thats 16 3 times negative.
4. Is negative 12 and 6 minus 12 is 4 4 minus 7 is negative 3 so f of negative. 4 is equal to negative 3.
So thats the first answer i believe my math is correct. I dont think i made any mistakes on that now lets evaluate f of zero zero.
Is between negative one and two so we need to use five x. Plus. Six.
So. This is going to be five times zero plus six five times 0. Is 0 0.
Plus. 6 is 6. Now what about the next one f of 2 now when x is exactly.
2. The function is equal to 12 so f of 2 is 12. Theres no math involved in that step now what about the last one f of 3.
When x is 3. We need to use x cubed plus. 4.
Because thats when x is greater than 2. When x is 3. So therefore.
This is going to be 3 raised to the third power plus. 4. So.
3 to the third power is 27 27. Plus. 4.
Is equal to 31. And that covers that problem. .
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