Demystify College Algebra with Step-by-Step Examples and Expert Guidance

g is related to one of the six parent functions. (a) Identify the parent function f. (b) Describe the sequence of transformations from f to g. (c) Sketch the graph of g by hand. (d) Use function notation to write g in terms of the parent function f. ${\displaystyle g\left(x\right)=-{(x+3)}^3-10}$

g is related to one of the parent functions. Describe the sequence of transformations from f to g. $g(x)=2-(x+5{)}^2$

Find the linear equations that can be used to convert an (x, y) equation to a (x, v) equation using the given angle of rotation θ. $\theta ={\tan }^{-1}(5/12)$

Find the linear equations that can be used to convert an (x, y) equation to a (x, v) equation using the given angle of rotation $\theta$ . $\theta ={70}^{\circ }$

g is related to one of the parent functions. Describe the sequence of transformations from f to g. $g(x)=-x^3-1$

Describe the transformations that were applied to $y=x^3$ to create each of the following functions.
a) ${\displaystyle y=12{(x-9)}^3-7}$
b) ${\displaystyle y=\left(\frac{7}{8}(x+1)\right)3+3}$
c) ${\displaystyle y=-2{(x-6)}^3-8}$
d) $y=(x+9)(x+9)(x+9)$
e) ${\displaystyle y=-2{(-3(x-4))}^3-5}$
f) ${\displaystyle y={\left(\frac{3}{4}(x-10)\right)}^3}$