How does the graph of g(x) = (x − 1)3 + 5 compare to the parent function f(x) = x3?

The original function was transformed by a a horizontal shift to the right in 1 unit, and also a vertical shift upwards of 5 units.

Step-by-step explanation:

Recall the four very important rules regarding translations (shifts) of the graph of functions:

1) In order to shift the graph of a function vertically c units upwards, we must transform  f (x) by adding c to it.

2) In order to shift the graph of a function vertically c units downwards, we must transform  f (x) by subtracting c from it.

3) In order to shift the graph of a function horizontally c units to the right, we must transform the variable x by subtracting c from x.

4) In order to shift the graph of a function horizontally c units to the left, we must transform the variable x by adding c to x.

We notice that in our case, The original function has been transformed by "subtracting 1 unit from x", and by adding 5 units to the full function. Therefore we are in the presence of a horizontal shift to the right in 1 unit (as explained in rule 3), and also a vertical shift upwards of 5 units (as explained in rule 1).

answer: a and c are correct

step-by-step explanation:

the +5 is the vertical translation

the added negative symbol in front is the reflection over the y-axis

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3