Many gas stations give a discount for using cash instead of a credit card. A gas station gives a discount of 10 cents per gallon
1 answer:
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Answer:
D.
Step-by-step explanation:
We are given the graph of the transformed tangent function.
As, we can see that the graph is shifted 2 units upwards.
That is, the parent function is translated 2 units up.
So, the new function will be of the form, .
Thus, options A and C are not correct.
Moreover, 'If a function f(x) has period P, then the function cf(bx) will have period .
Also, form the figure, we see that the period of the graphed function is .
Since, have period
.
So, function in option B will have period , which is not possible.
<em>Further, function in option D have period .</em>
Thus, the equation of the graphed function is, .
Answer:
We want a polynomial of smallest degree with rational coefficients with zeros in ,
and -3. The last root gives us the factor (x+3). Hence, our polynomial is
where is a polynomial with rational coefficients and roots
and
. The root
gives us a factor
, but in order to obtain rational coefficients we must consider the factor
.
An analogue idea works with . For convenience write
. This gives the factor
. Hence,
Notice that . So, in order to satisfy the last condition we divide by 3 the whole polynomial, without altering its roots. Finally, the wanted polynomial is
Step-by-step explanation:
We must have present that any polynomial it's determined by its roots up to a constant factor. But here we have irrational ones, in order to eliminate the irrational coefficients that a factor of the type will introduce in the expression, we need to multiply by its conjugate
. Hence, we will obtain
that have rational coefficients. Finally, the last condition is given with the intention to fix the constant factor. Usually it is enough to evaluate in the point and obtain the necessary factor.