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.

Consider the following. \[ \begin{array}{l}P(x)=\frac{1-5 x}{1-x} \\ \text { (a) State the domain of the function. } \\ \text { all real numbers } x \text { except } x=\frac{1}{5} \\ \text { all real numbers } x \text { except } x=-\frac{1}{5} \\ \text { all real numbers } x \text { except } x=-1 \\ \text { all real numbers } x\end{array} \] all real numbers \( x \) except \( x=1 \)

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 \( \quad(x, y)=(\square) \)

257. Funksiýalaryň grafigini guruñ: \( \begin{array}{ll}\text { a) } y=x^{2}+6 x ; & \text { c) } y=0,5 x^{2}-4 \\ \text { b) } y=-\frac{1}{2} x^{2}+2 ; & \text { d) } y=\frac{1}{2} x^{2}-3 x\end{array} \)

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 \( h(t)=-t^{2}+16 t+936 \).

Consider the following. \[ \begin{array}{l}g(x)=\frac{5 x}{x^{2}+4 x-5} \\ \text { (a) State the domain of the function. } \\ \text { all real numbers } x \text { except } x=5 \\ \text { all real numbers } x \text { except } x=1 \\ \text { all real numbers } x \text { except } x=-5 \\ \text { all real numbers } x \text { except } x=-5 \text { and } x=1 \\ \text { (b) Identify all intercepts. (If an answer does not exist, enter DNE.) } \\ x \text { except } x=0 \\ x \text {-intercept } \quad(x, y)=(\square) \\ y \text {-intercept } \quad(x, y)=(\square)\end{array} \]