As you can see in the image I made the example with n=6. In general, if the interval is divided into n equal parts we have that te right value of x in the kth rectangle (Rk) is
Rk = 2+ (1/2)k
So, f(Rk) = f(2+(1/2)k) = 2(2+(1/2)k)+1 = 4+k+1 = 5+k.
By "<span>f(x = 2x + 1" you likely meant "f(x) = 2x + 1."
The given interval is [2,5], and so the width of each interval is (5-2)/n, or (3/n). Since we are using right end points, the x value at the right endpoint of the kth rectangle is 2+k(3/n). Examples: if k=1, the value at the right endpoint is 2+1(3/n); if k=2, 2+2(3/n), and so on. If k=n, then the value at the right endpoint is 2+n(3/n), or 2+3=5, which agrees with the given interval [2,5].
Once again, the given function is f(x) = 2x + 1. At x = 2+k(3/n), the value of the function is 2[2+k(3/n)] + 1 (Answer). Check: If k=n, x = 2 + n(3/n) = 2+3 + 5, and f(5)=2(5) + 1 = 11.</span>
Step 1: Make sure that the trinomial is written in the correct order; the trinomial must be written in descending order from highest power to lowest power.
Step 2 : Decide if the three terms have anything in common, called the greatest common factor or GCF. If so, factor out the GCF. Do not forget to include the GCF as part of your final answer.
Step 3 : Multiply the leading coefficient and the constant, that is multiply the first and last numbers together.
Step 4 : List all of the factors from Step 3 and decide which combination of numbers will combine to get the number next to x.
Step 5 : After choosing the correct pair of numbers, you must give each number a sign so that when they are combined they will equal the number next to x and also multiply to equal the number found in Step 3.
Step 6 : Rewrite the original problem with four terms by splitting the middle term into the two numbers chosen in step 5.
Step 7 : Now that the problem is written with four terms, you can factor by grouping.
Functions can be classified by the operations they contain. Remember the following functions:
Power function has as its main operation of an exponent on the variable.
Root function has as its main operation a radical.
Log function has as its main operation a log.
Trig function has as its main operation sine, cosine, tangent, etc.
Rational exponent has as its main function division by a variable.
Exponential function has as its main operation a variable as an exponent.
Polynomial function is similar to a power function. It has as its main function an exponent of 2 or greater on the variable.
Below is listed each function. The bolded choice is the correct type of function:
(a) y = x − 3 / x + 3 root function logarithmic function power function trigonometric function rational function exponential function polynomial function of degree 3
(b) y = x + x2 / x − 2 power function rational function algebraic function logarithmic function polynomial function of degree 2 root function exponential function trigonometric function
(c) y = 5^x logarithmic function root function trigonometric function exponential function polynomial function of degree 5 power function
(d) y = x^5 trigonometric function power function exponential function root function logarithmic function
(e) y = 7t^6 + t^4 − π logarithmic function rational function exponential function trigonometric function power function algebraic function root function polynomial function of degree 6
(f) y = cos(θ) + sin(θ) logarithmic function exponential function root function algebraic function rational function power function polynomial function of degree 6 trigonometric function
