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3 years ago

Using the graph of f(x) below, find limit as x approaches negative 1 of f of x. (4 points)

Mathematics

1 answer:

Rama09 [41]3 years ago

7 0

Answer:

The limit of the function as x approaches to -1, is -1 and the option 4 is correct.

Step-by-step explanation:

According the the definition of limit, if,

$L=\lim_{x\rightarrow a^+}f(x)=\lim_{x\rightarrow a^-}f(x)$

Then the limit of function exist. Either the function is defined or not on the point a. If the at point a the value value of function is L, then the function is continuous.

From the given graph it is easily noticed that the value of f(x) approaches to -1 as x approaches to -1 from left or left. At x=-1 there is a open circle on (-1,-1), therefore this is not included in the function.

The value of f(x) is 2 at x=-1 because of the point (-1,-2).

$\lim_{x\rightarrow -1^+}f(x)=\lim_{x\rightarrow -1^-}f(x)=-1$

Therefore the limit of the function exist and the limit of the function is -1.

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The wall of a shower in a bathroom is 2 m high and 1.5 m wide. a (a) What is the area of the wall, in m²?? (b) What is the area

Allisa [31]

(A) 3m^2
(B) 30000cm^2
(C) 225cm^2
(D) 144
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3 years ago

Which statements about the graph of the function f(x) = -x2 - 4x + 2 are true? Select three options.

Nady [450]

Answer:

Domain is all real numbers.

The range is $\{y|y\le 6\}$

The function is increasing over $(-\infty,-2)$ .

The function is decreasing over $(-2,\infty)$

The function has a positive y-intercept.

-----------------This is a guess if I had interpreted your choices correctly:

Second option: The range is $\{y|y\le 6\}$

Third option: The function is increasing over $(-\infty,-2)$ .

Last option: The function has a positive y-intercept.

I can't really read some of your choices. So you can read my above and determine which is false. If you have a question about any of what I said above please let me know.

Note: I guess those 0's are suppose to be infinities? I hopefully your function is $f(x)=-x^2-4x+2$ .

Step-by-step explanation:

$f(x)=-x^2-4x+2$ is a polynomial function which mean it has domain of all real numbers. All this sentence is really saying is that there exists a number for any value you input into $-x^2-4x+2$ .

Now since the is a quadratic then it is a parabola. We know it is a quadratic because it is comparable to $ax^2+bx+c$ , $a \neq 0$ .

This means the graph sort of looks like a U or an upside down U.

It is U, when $a>0$ .

It is upside down U, when $a$ .

So here we have $a=-1$ so $a$ which means the parabola is an upside down U.

Let's look at the range. We know the vertex is either the highest point (if $a$ ) or the lowest point (if $a>0$ ).

The vertex here will be the highest point, again since $a$ .

The vertex's x-coordinate can be found by evaluating $\frac{-b}{2a}$ :

$\frac{-(-4)}{2(-1)}=\frac{4}{-2}=-2$ .

So the y-coordinate can be found by evaluate $-x^2-4x+2$ for $x=-2$ :

$-(-2)^2-4(-2)+2$

$-(4)+8+2$

$4+2$

$6$

So the highest y-coordinate is 6. The range is therefore $(-\infty,6]$ .

If you picture the upside down U in your mind and you know the graph is symmetrical about x=-2.

Then you know the parabola is increasing on $(-\infty,-2)$ and decreasing on $(-2,\infty)$ .

So let's look at the intevals they have:

So on $(-\infty,-2)$ the function is increasing.

Looking on $(-4,\infty)$ the function is increasing on (-4,-2) but decreasing on the rest of that given interval.

The function's y-intercept can be found by putting 0 in for $x$ :

$-(0)^2-4(0)+2$

$-0-0+2$

$0+2$

$2$

The y-intercept is positive since 2>0.

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3 years ago

Which is an advantage of using equations for solving problems?

Arisa [49]

Answer:

D.Every problem needs an equation in order to be able to solve it

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3 years ago

Read 2 more answers

Dave, Frida, Natalie, and Robbie have four adjacent seats at a baseball park. They randomly chose an order to sit in. Make a lis

Novosadov [1.4K]

The sample space (list of outcomes) is:
DFNR; DFRN; DRFN; DRNF; DNFR; DNRF;
NFDR; NFRD; NRFD; NRDF; NDRF; NDFR;
RFDN; RFND; RNFD; RNDF; RDFN; RDNF;
FRDN; FRND; FNRD; FNDR; FDRN; FDNR

P(Dave beside Natalie) = 1/2
P(B,G,B,G or G,B,G,B) = 1/3
P(boys in the middle) = 1/6
P(Frida beside Natalie) = 1/2
P(Robbie between Frida & Natalie) = 1/6
P(Natalie between Dave & Robbie) = 1/6

Explanation
Letting D=Dave, R=Robbie, N=Natalie, and F=Frida you get the list of possibilites above.

For P(Dave beside Natalie), look for DN or ND. This appears 12 times out of the 24 possibilities above; 12/24 = 1/2.

For P(B,G,B,G or G,B,G,B), we have the possibilities DFRN, DNRF, RFDN, RNDF, FRND, FDNR, NDFR, NRFD. There are 8 possibilites out of 24; 8/24 = 1/3.

For P(Frida beside Natalie), look for NF or FN. This appears 12 times out of the 24 possibilities; 12/24 = 1/2.

For Robbie between Frida and Natalie, look for FRN or NRF. This appears 4 times out of 24; 4/24 = 1/6.

For Natalie between Robbie and Dave, look for RND or DNR. This appears 4 times out of 24; 4/24 = 1/6.

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3 years ago

Charlie is a car salesman he earns $800 plus a 9% commission on all of her sales for the week if charlie receive the payment for

Westkost [7]

800+ (1960•.09) = 800+176.4=$976.40

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3 years ago