After several attempts I am unable ot solve. State the function that is finally graphed after the following transformations are applied to the graph of y=x^2. The graph is stretched vertically by a factor of 2, reflected across the x-axis, shifted left 1 units and shifted up 3 units. My incorrect answer was: 2f(-X)= (x+1)+3. Can you help me with this problem?
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pre-calc
- Thread starter adiz910
- Start date
State the function that is finally graphed after the following transformations are applied to the graph of y=x^2. The graph is stretched vertically by a factor of 2, reflected across the x-axis, shifted left 1 units and shifted up 3 units. My incorrect answer was: 2f(-X)= (x+1)+3.
How about this:
y/2 = -(x + 1)^2 +3
Please graph it to check for accuracy.
Hello, adiz910!
You should be able to "walk" through it . . .
\(\displaystyle \begin{array}{ccc} \text{We are given:} & y \:=\:x^2 \\ \\ \text{(1) stretched vertically by a factor of 2} & y \:=\:2x^2 \\ \\ \text{(2) reflected across the x-axis} & y \:=\:-2x^2 \\ \\ \text{(3) shifted left 1 unit} & y \:=\:-2(x+1)^2 \\ \\ \text{(4) and shifted up 3 units} & y \:=\:-2(x+1)^2 + 3 \end{array}\)
Why are both of you placing the "2" on the left side?
They asked for "the function" . . . not "twice the function" or "half the function".
.
You should be able to "walk" through it . . .
State the function that is finally graphed after the following transformations are applied to the graph of \(\displaystyle y\:=\:x^2\)
(1) The graph is stretched vertically by a factor of 2,
(2) reflected across the x-axis,
(3) shifted left 1 unit,
(4) and shifted up 3 units.
\(\displaystyle \begin{array}{ccc} \text{We are given:} & y \:=\:x^2 \\ \\ \text{(1) stretched vertically by a factor of 2} & y \:=\:2x^2 \\ \\ \text{(2) reflected across the x-axis} & y \:=\:-2x^2 \\ \\ \text{(3) shifted left 1 unit} & y \:=\:-2(x+1)^2 \\ \\ \text{(4) and shifted up 3 units} & y \:=\:-2(x+1)^2 + 3 \end{array}\)
Why are both of you placing the "2" on the left side?
They asked for "the function" . . . not "twice the function" or "half the function".
.