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3 years ago

Which polynomial function could be represented by the graph below?

Mathematics

1 answer:

Zinaida [17]3 years ago

6 0

Answer:

third answer

Step-by-step explanation:

The end behavior of the function indicates that the leading coefficient of x is negative (as x approaches infinity, f(x) approaches negative infinity for cubic functions with negative leading coefficients). This eliminates the first 2 answers. Next, factor out the common factor from the 3rd answer and set it to 0 to see if the roots of the polynomial shown on the graph (x=-3, x=2) match that of the answer.

factor out -2x since each term in the 3rd answer is divisible by -2x => -2x(x^2+x-6)

set the factored polynomial equal to 0 => -2x(x^2+x-6)
divide both sides by -2x => 0 = x^2+x-6
factor => (x+3)(x-2) = 0
find zeros by setting both factors equal to 0 => x=-3, x=2

This means that the 3rd answer is correct. The last answer, while having the correct leading coefficient, will produce roots of 3 and -2 instead of -3 and 2, which is shown on the graph.

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The graph shows the relationship between hours worked and total earnings for a store clerk. Let h represent hours worked and e r

Dovator [93]

Answer:

The answer is C.

Step-by-step explanation:

y = kx → e =

h → e = 7.5h

The independent variable is hours worked, h, and the dependent variable is total earnings, e. The independent variable is the input value of a function. The dependent variable is the output value of a function.

8 0

3 years ago

The line tangent to the graph of g(x) = x^{3}-4x+1 at the point (2, 1) is given by the formula

Usimov [2.4K]

well, about A and D, I just plugged the values on the slope formula of

$\bf \begin{array}{llll} g(x)=x^3-4x+1\\ L(x) = 8(x-2)+1 \end{array} \qquad \begin{cases} x_1=1.9\\ x_2=2.1 \end{cases}\implies \cfrac{f(b)-f(a)}{b-a}$

for A the values are 8.01 and 8.0, so indeed those "slopes" are close. $\textit{\huge \checkmark}$

for D the values are -2.25 and 8.0, so no dice on that one.

for B, let's check the y-intercept for g(x), by setting x = 0, we end up g(0) = 0³-4(0)+1, which gives us g(0) = 1.

checking L(x) y-intercept, well, L(x) is in slope-intercept form, thus the +1 sticking out on the far right is the y-intercept, so, dice. $\textit{\huge \checkmark}$

for C, well, the slope if L(x) is 8, since it's in slope-intercept form, the derivative of g(x) is g'(x) = 3x² - 4, and thus g'(0) = -4, so no dice.

for E, do they intercept at (2,1)? well, come on now, L(x) is a tangent line to g(x), so that's a must for a tangent. $\textit{\huge \checkmark}$

for F, we know the slope of the line L(x) is 8, is g'(2) = 8? let's check

recall that g'(x) = 3x² - 4, so g'(2) = 3(2)² - 4, meaning g'(2) = 8, so, dice. $\textit{\huge \checkmark}$

6 0

3 years ago

A medical center observed that about 60% of its morning appointments were with elderly patients. The table shows the results of

Marta_Voda [28]

50% because of your question so the answer is 50%

7 1

3 years ago

Help please it’s due soon <br><br> ( DISTANCE IS A MISTAKE )

katrin [286]

Answer:

speed

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You can fill in these words in the blanks.

4 0

3 years ago

4. Six numbers are shown.

Reptile [31]

Step-by-step explanation:

sorry i couldn't solve the last and the last second one

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If there is any kind of suspicious mistake

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7 0

3 years ago