Functions › Graphs, intersections and asymptotes

Asymptotes

Degree of numerator for horizontal asymptote ●○○○○ 10 ptsThe graph of the rational function $\frac{q(x)}{2x^5+x^4-7x^2+1}$ has a horizontal asymptote. What is the largest possible degree of $q(x)$ ?
Sum of vertical asymptotes ●○○○○ 10 ptsThe graph of $y=\frac{5x^2-9}{3x^2+5x+2}$ has vertical asymptotes at $x = a$ and $x = b$ . Find $a + b$ . Round to two decimal places.
Horizontal asymptote of a rational function ●○○○○ 10 ptsAt what value of $y$ is there a horizontal asymptote for the graph of the equation $y=\frac{4x^3+2x-4}{3x^3-2x^2+5x-1}$ ? Round to two decimal places.
Crossing the horizontal asymptote ●●○○○ 20 ptsFor which value of $x$ does the function $f(x) = \frac{2x^2 - 5x - 7}{x^2 - 4x + 1}$ cross its horizontal asymptote?
Horizontal tangent of a rational function ●●○○○ 20 ptsThe graph of $f(x)=\frac{ax+b}{(x-1)(x-4)}$ has a horizontal tangent line at $(2,-1)$ . Determine the values of $a$ and $b$ .
Rational function with horizontal tangent ●●○○○ 20 ptsThe graph of $g(x) = \frac{ax+b}{(x-1)(x-4)}$ passes through the point $(2,-1)$ and has a horizontal tangent there. Find the values of $a$ and $b$ .
Parameter sum for a symmetric rational function ●●●○○ 50 ptsGiven the function $f(x)=\frac{x}{ax+b}$ with $a\neq 0$ , its graph passes through the point $(-4,4)$ and is symmetric about the line $y=-x$ . Find the value of $a+b$ . Give your answer as a decimal.
Rational function symmetric about y=-x ●●●○○ 50 ptsGiven the function $f(x)=\frac{x}{ax+b}$ with $a\neq 0$ , the graph passes through the point $(-4,4)$ and is symmetric about the line $y=-x$ . Find the value of $a+b$ . Give your answer as a decimal.

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