Translations of Functions

If a function is translated right 1 unit and up 5 units, what is the equation of the transformed function?

• @@f(x) = (x - 1) + 5@@

• @@f(x) = (x + 1) + 5@@

• @@f(x) = (x - 1) + 3@@

• @@f(x) = (x + 1) + 3@@

What is the equation for the translation of @@f(x)=|x|@@ that moves up 6 units?

• @@f(x)=|x|+6@@

• @@f(x)=|x|-6@@

• @@f(x)=|x|+3@@

• @@f(x)=|x|+2@@

If f(x) = 2x+5 is translated right 2 units, what is the new equation?

• @@2(x-2)+5@@

• @@2x+5+2@@

• @@2(x+2)+5@@

• @@2x+5-2@@

What is the new equation of @@f(x)=\frac{1}{x}@@ after translating it 2 units down?

• @@f(x)=\frac{1}{x}-2@@

• @@f(x)=\frac{1}{x}+2@@

• @@f(x)=\frac{1}{x}-1@@

• @@f(x)=\frac{1}{x}-3@@

What would the transformed equation of @@y=x^{2 ext{ }}+4x+3@@ be with a horizontal shift to the left 2 units?

• @@y=ig(x+2ig)^{2 ext{ }}+4ig(x+2ig)+3@@

• @@y=x^{2}+4x+3+2@@

• @@y=ig(x-2ig)^{2 ext{ }}+4ig(x-2ig)+3@@

• @@y=ig(x+2ig)^{2 ext{ }}+4ig(x+2ig)+5@@

What is the effect of a horizontal translation on the graph of a function?

• It shifts the graph up or down depending on the value added or subtracted.

• It shifts the graph left or right depending on the sign of the value added or subtracted.

• It reflects the graph over the x-axis.

• It stretches the graph vertically or horizontally.

How does a horizontal shift affect the equation of @@f(x)= ext{sqrt}(x)@@ when shifted 3 units to the left?

• @@f(x)= ext{sqrt}(x+3)@@

• @@f(x)= ext{sqrt}(x-3)@@

• @@f(x)= ext{sqrt}(x) + 3@@

• @@f(x)= ext{sqrt}(x) - 3@@

What is the equation of a quadratic function translated left 4 units from the standard form @@y=x^{2}@@?

• @@y=(x+4)^{2}@@

• @@y=(x-4)^{2}@@

• @@y=(x+2)^{2}@@

• @@y=(x-2)^{2}@@

How do you write the equation of a function after a translation?

• You replace x with (x - h) or (x + h) for horizontal shifts and add or subtract 'k' for vertical shifts.

• You replace x with (x + h) for horizontal shifts and multiply by 'k' for vertical shifts.

• You replace x with (x - h) for horizontal shifts and divide by 'k' for vertical shifts.

• You keep x the same and only change the function's output value for vertical shifts.