What causes the graph of \( y=x^{2} \) to open downward?

Write the expression as a single logarithm. \[ 2 \log _{a}\left(6 x^{3}\right)-\frac{1}{3} \log _{a}(2 x+13) \] \( 2 \log _{a}\left(6 x^{3}\right)-\frac{1}{3} \log _{a}(2 x+13)=\square \) (Simplify your answer.)

Find the function rule for \( g(x) \). The function \( f(x)=x^{2} \). The graph of \( g(x) \) is \( f(x) \) translated to the right 7 units and up 3 units. What is the function rule for \( g(x)^{\text {? }} \) \[ g(x)=(x+3)^{2}-7 \] o \( g(x)=(x-7)^{2}+3 \) \( g(x)=(x+7)^{2}-3 \) \( g(x)=(x-3)^{2}+7 \)

1at transformations change the graph of \( f(x) \) to the graph of \( g(x) \) ? \( x)=-5 x^{2} g(x)=-20 x^{2}-8 \) The graph of \( g(x) \) is the graph of \( f(x) \) stretched vertically by a factor of \( \frac{1}{4} \) and translated down 8 units. b the graph of \( g(x) \) is the graph of \( f(x) \) stretched vertically by a factor of 4 and translated down 8 units. The graph of \( g(x) \) is the graph \( f(x) \) of stretched vertically by a factor of \( \frac{1}{4} \) and translated up 8 units.

\( \begin{array}{ll}\begin{array}{l}\text { Crude oil may contain hundreds of different types } \\ \text { of hydrocarbons. Some examples include: }\end{array} & \begin{array}{l}\text { Identify each of the highighted materials as an } \\ \text { element, a compound, or a mixture, and explain } \\ \text { your reasoning. }\end{array} \\ \text { - Butane }\left(\mathrm{C}_{4} \mathrm{H}_{10}\right) & \\ \text { - Dodecane }\left(\mathrm{C}_{12} \mathrm{H}_{26}\right) & \\ \text { - Benzene }\left(\mathrm{C}_{6} \mathrm{H}_{6}\right) & \\ \text { Many common fuels, such as gasoline and } \\ \text { kerosene, are combinations of these substances } \\ \text { or others. When these fuels burn, they combine } \\ \text { with oxygen }\left(\mathrm{O}_{2}\right) \text { to produce carbon dioxide }\left\{\mathrm{CO}_{2}\right) & \\ \text { and water }\left(\mathrm{H}_{2} \mathrm{O}\right) \text {. }\end{array} \)

v) \( \frac{8}{7}: \frac{1}{23}-\frac{14}{21}: 23 \)