91Ó°ÊÓ

Find a formula for a function describing the given situation. Graph the function and give a domain that makes sense for the problem. Recall that with constant speed. distance \(=\) speed \(\cdot\) time elapsed or \(d=v t\) A function \(y=f(x)\) such that \(y\) is 1 less than the cube of \(x\)

Simplify the difference quotients\(\frac{f(x+h)-f(x)}{h}\) and \(\frac{f(x)-f(a)}{x-a}\) for the following functions. $$f(x)=2 x^{2}-3 x+1$$

Find a formula for a function describing the given situation. Graph the function and give a domain that makes sense for the problem. Recall that with constant speed. distance \(=\) speed \(\cdot\) time elapsed or \(d=v t\) A function \(y=f(x)\) such that if you run at a constant rate of \(5 \mathrm{mi} / \mathrm{hr}\) for \(x\) hours, then you run \(y\) miles

Simplify the difference quotients\(\frac{f(x+h)-f(x)}{h}\) and \(\frac{f(x)-f(a)}{x-a}\) for the following functions. $$f(x)=\frac{x}{x+1}$$

Draw a right triangle to simplify the given expressions. Assume \(x>0\) $$\cos \left(\sin ^{-1} x\right)$$

Draw a right triangle to simplify the given expressions. Assume \(x>0\) $$\cos \left(\sin ^{-1}(x / 3)\right)$$

Simplify the difference quotients\(\frac{f(x+h)-f(x)}{h}\) and \(\frac{f(x)-f(a)}{x-a}\) for the following functions. $$f(x)=x^{4}$$

Find a formula for a function describing the given situation. Graph the function and give a domain that makes sense for the problem. Recall that with constant speed. distance \(=\) speed \(\cdot\) time elapsed or \(d=v t\) A function \(y=f(x)\) such that if you ride a bike for \(50 \mathrm{mi}\) at \(x\) miles per hour, you arrive at your destination in \(y\) hours

Write the following logarithms in terms of the natural logarithm. Then use a calculator to find the value of the logarithm, rounding your result to four decimal places. $$\log _{6} 60$$

Simplify the difference quotients\(\frac{f(x+h)-f(x)}{h}\) and \(\frac{f(x)-f(a)}{x-a}\) for the following functions. $$f(x)=x^{3}-2 x$$