Functions (Adv)

Which of the following functions is odd?

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Which graph shows the solutions of  $\left|x-1\right|\le3\ ?$  

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Which of the following is the graph of  $y=\left|x+3\right|\ ?$  

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The functions  $y=f\left(x\right)$  and  $y=g\left(x\right)$  have been sketched. How many POSITIVE solutions does the equation  $f\left(x\right)=g\left(x\right)$   have?

• 0

• 1

• 2

• 3

Which of the following is true given that  $y=f\left(x\right)$  is an odd function?

•  $f\left(-x\right)=f\left(x\right)$  

•  $f\left(-x\right)=-2f\left(x\right)$  

•  $f\left(1\right)+f\left(-1\right)=0$  

•  $f\left(x\right)=0$  

What is the new equation when $y=3^x$  is rotated by  $180\degree$  about the origin?

•  $y=-3^x$  

•  $y=-3^{-x}$  

•  $y=9^{2x}$  

•  $-y=-3^{-x}$  

•  $y=3^{-x}$  

Given that curve B is the graph  $y=x^2$ , Which of the following would graph D be? 

•  $y=\frac{1}{8}x^2$  

•  $y=\frac{1}{2}x^2$  

•  $y=2x^2$  

•  $y=8x^2$  

•  $y=-x^2$  

Which of the following equations below is odd?

•  $f\left(x\right)=\frac{2^x+2^{-x}}{2}$  

•  $f\left(x\right)=\frac{2^x-2^{-x}}{2}$  

•  $f\left(x\right)=x^{\frac{2}{3}}$  

•  $f\left(x\right)=x\sqrt{9-x}$  

•  $f\left(x\right)=x^{\frac{1}{3}}+1$  

Given that  $f\left(x\right)=2x+3$  and  $g\left(x\right)=5x+b.$  Find the value of  $b$  so that  $g\left(f\left(x\right)\right)=f\left(g\left(x\right)\right)$ .

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• 12

The hyperbola  $y=\frac{1}{x}$  is shifted 2 units to the right. What is the equation of the new hyperbola?

•  $y=\frac{1}{x+2}$  

•  $y=\frac{1}{x-2}$  

•  $y=\frac{1}{x}+2$  

•  $y=\frac{1}{x}-2$  

•  $y=2-\frac{1}{x}$