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Instructions: Select the correct answer from each drop-down menu.

Graph the function y = f(x) = x2.

If the graph of the given function were shifted six units to the left, the new graph would represent the function,

A.) y=f(x+6) =(x+6)^2

B.) y=f(x-6)=(x-6)^2

C.) y=f(x)+6=x^2+6

D.) y=f(x)-6=x^2-6

If the graph of the given function were shifted upward by six units, the new graph would represent the function,

A.) y=f(x+6)=(x+6)^2

B.) y=f(x-6)=(x-6)^2

C.) y=f(x)+6=x^2+6

D.) y=f(x)-6=x^2-6

For the same y-values, the corresponding x-values of the function,

A.) y=f(3x/2)=(3x/2)^2

B.) y=f(2x/3)=(2x/3)^2

C.) y=f(x+1.5)=(x+1.5)^2

D.) y=f(x)+1.5=x^2+1.5

are 1.5 times of the x-values of the function y = f(x) = x2.

Verified Answer :

bcalle

The answers are A, C, A in the order they are listed

Answer:

1) Option A

2) Option C

3) Option A

Step-by-step explanation:

We have given that :  function \(y=f(x)=x^2\)

1) If the graph of the given function were shifted six units to the left

translation to left means b unit is add on the function

i.e f(x)=f(x+b)

Therefore,the new graph have the function \(y=f(x+6)=(x+6)^2\)

so, Option A is correct

2) If the graph of the given function were shifted upward by six units

translation to upward means b unit is add to the function

i.e f(x)=f(x)+b

Therefore,the new graph have the function \(y=f(x)+6=x^2+6\)

so, Option C is correct

3) 1.5 times of the x-values of the function \(y=f(x)=x^2\)

1.5 times of the x-values means 1.5x = 3x/2

Therefore, \(y=f(3x/2)=(3x/2)^2\)

So,  Option A is correct

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