Exam 9: Logarithmic and Exponential Functions

Graph. State the domain, range, and horizontal asymptote of the function - $f(x)=3^{x}-2$

Solve. - $\log _{3}(-6-5 x)=2$

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions. - $f(x)=x+1$

Compute the compound interest. -How long must $\$ 5900$ be in a bank at $6 \%$ compounded annually to become $\$ 9967.93$ ? (Round to the nearest year.)

Solve the problem. -Find $\left(\frac{f}{g}\right)(-2)$ when $f(x)=2 x-7$ and $g(x)=4 x^{2}+14 x+3$ .

Solve. -The function $\mathrm{A}=\mathrm{A}_{0} \mathrm{e}^{-0.01386 \mathrm{x}}$ models the amount in pounds of a particular radioactive material stored in a concrete vault, where $\mathrm{x}$ is the number of years since the material was put into the vault. If 700 pounds of the material are plaœed in the vault, how much time will need to pass for only 152 pounds to remain?

Solve. Round to the nearest thousandth, if necessary - $13 ^x=23$

Determine whether the graph is the graph of a function. -

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions. - $f(x)=4-x$

For the given graph of a one-to-one function $f(x)$ , graph its inverse function $f^{-1}(x)$ using a dashed line. -

Determine whether function is one-to-one. - -2 -1 0 1 () -6 -6 2 -1

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers. - $\log _{7} 21-\log _{7} 17$

Determine whether function is one-to-one. -The function that pairs a student's ID number with their GPA.

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated - $f(x)=2 x^{2}+7 x-5, g(x)=7 x^{2}+3 x+9$ Find $(f+g)(x)$ .

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of thisfunction. - $f(x)=3^{x}+2$

Solve. Round to the nearest thousandth, if necessary - $5^{3 \mathrm{x}-2}=18$

Solve. - $3 x=27$

Solve. - $\log _{10} x=1$

Solve. Round to the nearest thousandth, if necessary - $e^{\mathrm{x}+8}=2$

Suppose for some base $b>0(b \neq 1)$ that $\log _{b} 2=A, \log _{b} 3=B, \log _{b} 5=C$ , and $\log _{b} 7=D$ . Express the given logarithms in terms of A, B, C, or D. - $\log _{b}\left(\frac{1}{4}\right)$