Answer to Question #193679 in Algebra for chris

Question

1.Sketch the graph that represents y=6log(x-7) + 2

https://lh4.googleusercontent.com/vEwh848sXA94dOj_DL12sGCfgXDI3l8rjJhXKAjI_Q-Uchbs3kZsaPRPgLOrj6n69i3veT3nJJ8MUKBNFzUUA9JTemem1lvlvg_2BzTPGMVF7ls1pB7MjvRowIpBE_9sBu-fNUUQ

2.Write the equation of the parent function y=³sqaure root of x includes the following transformations

a. Vertical compression of 1/5

b. Left 5

c. Down 8

Equation:

3.Use log properties to expand

a. log₇10x

b. log₂(x/5)

Answer 1

1.

the equation of the function is: $y=6\space log(x−7)+2$

2.

$y^3=\sqrt x$

a.

vertical compression of $\frac{1}{5}$

when we multiply a function by a positive constant

we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function.

$y^3=\frac{1}{5}\sqrt x$

b.

Left 5

To shift a function left, add inside the function argument; $f(x+b)$

$y^3=\sqrt{x+5}$

c.

down 8

$y^3=\sqrt x -8$

3.

a.

$log_710x$

Apply log rule: $log_c(ab)=log_c(a)+log_c(b)$

$log_7(10x)=log_7(10)+log_7(x)$

$=log_7(10)+log_7(x)$

b.

$log_2(\frac{x}{5})$

Apply log rule: $log_c(\frac{a}{b}) =log_c(a)-log_c(b)$

$log_2(\frac{x}{5})=log_2(x)-log_2(5)$