Q: the function y=csch(5 ln x) as a rational function is given by:
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- Now lets use a graphing calculator to get a graph of C=59(F32). By letting F=x and C=y, we obtain Figure 7.15. Pay special attention to the boundaries on x. These values were chosen so that the fraction (Maximumvalueofx)minus(Minimumvalueofx)95 Would be equal to 1. The viewing window of the graphing calculator used to produce Figure 7.15 is 95 pixels dots wide. Therefore, we use 95 as the denominator of the fraction. We chose the boundaries for y to make sure that the cursor would be visible on the screen when we looked for certain values. This was accomplished by setting the aforementioned fraction equal to 1 By moving the cursor to each of the F values, we can complete the table as follows. F 5 5 9 11 12 20 30 45 60 C 21 15 13 12 11 7 1 7 16 The C values are expressed to the nearest degree. Use your calculator and check the values in the table by using the equation C=59(F32).Consider the following rational functions: r(x)=x2x22x1 s(x)=x2+4x3+27 t(x)=x+2x39x u(x)=x225x2+x6 w(x)=x+3x3+6x+9x (a) Which of these rational functions has a horizontal asymptote? (b) Which of these functions has a slant asymptote? (c) Which Of these functions has no vertical asymptote? (d) Which Of these functions has a "hole"? (e) What are the asymptotes of the function r(x) ? (f) Graph y =u(x) , showing clearly any asymptote and x- and y intercepts the function may have. (g) Use long division to find a polynomial P that has the same end behavior as t. graph both P and t on the same screen to verify that they have the sane end behavior.If the rational function y r1x2 has the horizontalasymptot
- Find the x- and y-intercepts of the rational function. (If an answer does not exist, enter DNE.) t(x) = x2 − 2x − 15 x − 8 x-intercept (x, y) = (smaller x-value) x-intercept (x, y) = (larger x-value) y-intercept (x, y) =find the x- and y-interceptsofthe rational function. (if an answer does not exist, enter DNE.) t(x)=x^2-2x-15/x-9 x-intercept (x,y)= (smaller x-value) x-intercept (x,y)= (larger x-value) y-intercept (x,y)=Find the x- and y-intercepts of the rational function. (If an answer does not exist, enter DNE.) r(x) = x2 − 4 x2 x-intercept (x, y) = (smaller x-value) x-intercept (x, y) = (larger x-value) y-intercept (x, y) =
- The following question is about the rational function r(x) = (x + 1)(x − 3) (x + 3)(x − 7) . The function r has x-intercepts (smaller value) and (larger value).Create a rational function that has the followingcharacteristics: crosses the x-axis at 3; touches the x-axisat - 2; one vertical asymptote, x = 1; and one horizontalasymptote, y = 2. Give your rational function to a fellowclassmate and ask for a written critique of your rationalfunction.find the x- and y-intercepts of the rational function. (if an answer does not exist, enter DNE.) r(x)= x^2-9/x^2 x-intercept (x,y)= (smaller x-value) x-intercept (x,y)= (largerx-value) y-intercept (x,y)=
- What is the equation for the horizontal asymptote of the rational functional graph? 1) y=2 2)Y=3 3)Y=0 4)X=3 5)X=2 6)X=0In a rational function, as x⟶∞,y⟶∞. It follows that the rational function has ___________ Suppose that the graph of a rational function intersects the y - axis at y=b.y=b. It follows that the ____________ of the function is b. As x→c,y→∞.x→c,y→∞. In this case, we say that the line x=cx=c is a __________ of a rational function.