Question

Let f(x) = -9 logo (x + 3) + 5. Graph f(a) using transformations. (a) Identify the transformations used to graph f(x). Select all that apply. horizontally stretched vertically stretched shifted right 3 units shifted left 3 units vertically compressed shifted up 5 units reflected over the y-axis shifted up 5 units shifted down 5 units shifted left 5 units reflected over the z-axis shifted right 5 units shifted down 5 units horizontally compressed (b) Identify the important point of f(x). (c) Identify the horizontal asymptote of f(x). y = > Next Question

Answer 1

we are given

$f(x)=-9log_6(x+3)+5$

(a)

we have parent function as

$y=log_6(x)$

There is x+3

so,

it is shifted left side by 3 units

+5 is added

so,

it is shifted upward by 3 units

negative sign is multiply to log

so, it is reflected about x-axis

9 is multiplied to log

so, it is vertically stretch by 9 units

(b)

Graph:

-5 y = -9 logo (x + 3)+5 (-0.294,0) TT -3 -2 2 3 4 (0, -0.518) on

Important points:

$(x,y)=(-0.294,0)$

$(x,y)=(0,-0.518)$

(c)

Since, there is only vertical asymptote for this function

so, horizontal asymptote does not exist.......................Answer