Question

How many discontinuities does the following piecewise function have? \begin{cases} 3e^{x+3} + 1, & x < -3 \\ \frac{2}{3}x^2 - 1, & -3 \le x \le 3 \\ -\frac{7}{2}x + \frac{29}{2}, & 3 < x < 5 \\ \log(2x - 4), & x \ge 5 \end{cases} three two one zero Score 0

          How many discontinuities does the following piecewise function have?
\begin{cases}
3e^{x+3} + 1, & x < -3 \\
\frac{2}{3}x^2 - 1, & -3 \le x \le 3 \\
-\frac{7}{2}x + \frac{29}{2}, & 3 < x < 5 \\
\log(2x - 4), & x \ge 5
\end{cases}
three
two
one
zero
Score
0
        
Show more…
How many discontinuities does the following piecewise function have?

3e^x+3 + 1,     x < -3 

(2)/(3)x^2 - 1,     -3 ≤x ≤3 

-(7)/(2)x + (29)/(2),     3 < x < 5 

log(2x - 4),     x ≥5

three
two
one
zero
Score
0

Added by Tamara Y.

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Precalculus with Limits
Precalculus with Limits
Ron Larson 2nd Edition
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How many discontinuities does the following piecewise function have? f(x)={(3e^(x+3)+1,x<-3),((2)/(3)x^(2)-1,-3=5):} three two one zero Score How many discontinuities does the following piecewise function have? 3e*+3+1, x<-3 fx= 13 29 x+ 2 [1og(2x-4), x5 three two one zero Score 0
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Transcript

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00:01 We want to know how many functions a given piecewise function have.
00:05 Well, if we're given a piecewise function, say f of x equals, and really, i'm just going to give two portions to the piecewise function, actually three portions.
00:17 We'll have x squared from zero to two, and then we'll have two x from two to four, and then we'll have two x from two to four, and then we'll have x cubed from four and on.
00:45 So where is the discontinuity? we know that with the discontinuity, the discontinuity will occur when the limit as x approaches c of f of x is not equal to f of c.
00:57 That's what a discontinuity means.
00:59 So in this case, we see that the limit as x approaches two from the left is four, and the limit as x approaches 2 from the right here is also 4...
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