Topic 2.4 - Exponential Function Manipulation

Which of the following functions is an equivalent form of the function $$y=9^{2x}$$

Which of the following functions is an equivalent form of the function $$y=9\cdot4^x$$

Let $$f\left(x\right)$$ be a function on which a transformation occurs. Let $$g\left(x\right)$$ be a transformation of f. Name the transformations of f.

$$f\left(x\right)=3^x\ and\ g\left(x\right)=f\left(x\right)\cdot27$$

​

Let $$f\left(x\right)$$ be a function on which a transformation occurs. Let $$g\left(x\right)$$ be a transformation of f. Name the transformations of f.

$$f\left(x\right)=9^x\ and\ g\left(x\right)=3^x$$

​

Let $$f\left(x\right)$$ be a function on which a transformation occurs. Let $$g\left(x\right)$$ be a transformation of f. Name the transformations of f.

$$f\left(x\right)=2^x\ and\ g\left(x\right)=\frac{f\left(x\right)}{16}$$

​

Let $$f\left(x\right)$$ be a function on which a transformation occurs. Let $$g\left(x\right)$$ be a transformation of f. Name the transformations of f.

$$f\left(x\right)=5^x\ and\ g\left(x\right)=\left(f\left(x\right)\right)^{-3}$$

​

Re-write the exponential function in the form $$y=ab^x$$ where a and b are positive constants.

$$f\left(x\right)=7^{x+2}$$

Re-write the exponential function in the form $$y=ab^x$$ where a and b are positive constants.

$$n\left(x\right)=8^{\frac{x}{3}}$$

Re-write the exponential function in the form $$y=ab^x$$ where a and b are positive constants.

$$m\left(x\right)=2\left(4\right)^{x-1}$$

Evaluate the function at the given input.

Let $$h\left(x\right)=2\cdot3^{\frac{x}{2}}$$ find $$h\left(1\right)$$

Give an exact answer.