tarting with the graph of \( f(x)=7^{x} \), write the formula for the function that results from (a) shifting \( f(x) 4 \) units downward, \( y=\square \) (b) shifting \( f(x) 5 \) units to the right, \( y=\square \) (c) reflecting \( f(x) \) about the \( x \)-axis, \( y=\square \)

Consider the following. \[ \begin{array}{l}g(x)=\frac{6(x+3)}{x(x-6)} \\ \text { (a) State the domain of the function. } \\ \text { all real numbers } x \text { except } x=3 \text { and } x=6 \\ \text { all real numbers } x \text { except } x=0 \text { and } x=6 \\ 0 \text { all real numbers } x \text { except } x=-3 \text { and } x=6 \\ 0 \text { all real numbers } x \text { except } x=0 \text { and } x=3 \\ \text { all real numbers } x \\ \text { (b) Identify all intercepts. (If an answer does not exist, enter DNE.) } \\ x \text {-intercept } \quad(x, y)=(\square)\end{array} \] \( y \)-intercept \( \quad(x, y)=(\square) \)

Consider the following. \[ f(x)=\frac{3 x^{2}-19 x+20}{3 x^{2}-x-70} \] (a) State the domain of the function. all real numbers \( x \) except \( x=\frac{4}{3}, 5 \) all real numbers \( x \) except \( x=-\frac{5}{3}, 14 \) all real numbers \( x \) except \( x=-\frac{14}{3}, 5 \) all real numbers \( x \) except \( x=-5, \frac{14}{3} \) Identify all intercepts; (If an answer does not exist, enter DNE.) \( x \)-intercept \( \quad(x, y)=(\square \)-intercept \( \quad(x, y)=(\square) \)

Unit 3 AsSessment Path of Lava Lava coming from the eruption of a volcano follows a parabolic path. The height \( h \) in feet of a piece of lava \( t \) seconds after it is ejected from the volcano is given by \( h(t)=-t^{2}+16 t+936 \).

Постройте график функции и укажите для нее область определения и значения \( x \), при которых \( y>0 \). а) \( у=3 \mathrm{x}^{-3} \);

Consider the following. \[ f(x)=\frac{x^{2}+4}{x+1} \] (a) State the domain of the function. (b) Identify all intercepts. (c) Find any vertical and slant asymptotes. (d) Plot additional solution points as needed to sketch the graph of the rational function.