Precalculus Transformations of Graphs Quiz: 10 Questions with Explanations

A Shifted right 5B Shifted left 5C Shifted up 5D Shifted down 5

The h in (x – h) is 5, so the graph moves right. A minus inside moves right.

A \(y=f(-x)\)B \(y=-f(-x)\)C \(y=f(x)-1\)D \(y=-f(x)\)

A negative outside the function flips the sign of every output.

A \((3,1)\)B \((1,1)\)C \((1,5)\)D \((3,5)\)

x + 1 inside moves the graph left 1, so x becomes 1; the -2 moves y down to 1.

A Horizontal stretch by 3B Shift up 3C Vertical stretch by 3D Vertical compression by 3

Multiplying outputs by 3 stretches the graph vertically by a factor of 3.

A \(y=|x+2|-3\)B \(y=|x-2|-3\)C \(y=|x-2|+3\)D \(y=|x+2|+3\)

The vertex is (2, -3): right 2 and down 3.

A \(f(x)=x^{3}\)B \(f(x)=x^{2}+x\)C \(f(x)=x^{5}-x\)D \(f(x)=x^{4}+1\)

x^4 + 1 gives the same value for -x, so it is even.

A The one in the left half-planeB The one in the lower rightC The one in the upper rightD None of them

Replacing x by -x reflects over the y-axis, so the graph lies where x <= 0.

A \([-4,\infty)\)B \([4,\infty)\)C \((-4,\infty)\)D \([0,\infty)\)

x + 4 >= 0 gives x >= -4. The graph shifts left 4.

A \((1,5)\)B \((-1,5)\)C \((-1,-5)\)D \((1,-5)\)

Read (x – h) with h = -1 and k = 5. The sign on x + 1 is the opposite of h.

A WiderB Shifted up 2C NarrowerD Reflected over the x-axis

Multiplying by 2 doubles each height, making the parabola narrower.