Question #193679

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)



1
Expert's answer
2021-05-24T02:20:02-0400

1.

the equation of the function is: y=6 log(x7)+2y=6\space log(x−7)+2




2.

y3=xy^3=\sqrt x


a.

vertical compression of 15\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.

y3=15xy^3=\frac{1}{5}\sqrt x


b.

Left 5

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

y3=x+5y^3=\sqrt{x+5}


c.

down 8

y3=x8y^3=\sqrt x -8


3.

a.

log710xlog_710x

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

log7(10x)=log7(10)+log7(x)log_7(10x)=log_7(10)+log_7(x)

=log7(10)+log7(x)=log_7(10)+log_7(x)


b.

log2(x5)log_2(\frac{x}{5})

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

log2(x5)=log2(x)log2(5)log_2(\frac{x}{5})=log_2(x)-log_2(5)


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