Search problems

9 problems match “odd functions”. Clear

Visitors search a sample. Sign in for free to search every problem. Sign in

1. Value of an odd function ●○○○○ 10 ptsThe function $y=f(x)$ is an odd function, and $f(x)=3^x - 1$ for $x \geq 0$. Find $f(-2)$.
2. Odd function value at a positive point ●○○○○ 10 ptsGiven that $f(x)$ is an odd function, and when $x < 0$, $f(x) = x^3 + x^2$, find $f(2)$.
3. Value of an odd function shifted by a constant ●○○○○ 10 ptsGiven that $f(x)$ is an odd function, $g(x)=f(x)+6$, and $g(-1)=3$. Find $f(1)$.
4. Value of even plus odd function ●●○○○ 20 ptsLet $e(x)$ be an even function and let $o(x)$ be an odd function such that $e(x) + x^2 = o(x)$ for all $x$. Let $f(x) = e(x) + o(x)$. Find $f(2)$.
5. Even function on an interval ●●○○○ 20 ptsLet $f(x)=x^{2}+3ax+4$ be defined on the interval $b-3 \leq x \leq 2b$. Given that $f$ is an even function on this interval, find the value of $a-b$.
6. Area of a parallelogram on a log graph ●●●○○ 50 ptsGiven points $A(3,1)$ and $B\left(\frac{5}{3},2\right)$. The four vertices of parallelogram $ABCD$ all lie on the graph of $f(x)=\log_{2}\frac{ax+b}{x-1}$. Find the area of parallelogram $ABCD$. Round to two decimal places.
7. Roots of a symmetric odd function ●●●○○ 50 ptsLet $y=f(x)$ be an odd function defined on $\mathbf{R}$ whose graph is symmetric about the line $x=1$. When $0<x\leq 1$, $f(x)=\log_3 x$. Find the sum of all real roots of the equation $f(x)=-\frac{1}{3}+f(0)$ in the interval $(0,10)$.
8. Sum of values of a shifted odd function ●●●○○ 50 ptsGiven that $f(x)$ is an odd function defined on $\mathbb{R}$ and $f(1) = 1$. If the graph of $f(x)$ is translated one unit to the right, the resulting graph is that of an even function. Find the sum $f(1) + f(2) + f(3) + \ldots + f(2009)$.
9. Real roots of a sine-power equation ●●●●○ 100 ptsFind the number of real roots of the equation $\sin(2013\pi x)=x^{2013}$.