Question

A coordinate plane's axes range from negative 5 to 5, both by 1-unit increments. 2 functions are plotted, 1 solid and 1 dotted. The solid function is labeled 'Function upper A' and the dotted function is labeled 'Function upper B.'
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Function upper A is a concave up parabola. The curve passes through left parenthesis negative 2 comma 4 right parenthesis and through left parenthesis 2 comma 4 right parenthesis, with the function's minimum point at left parenthesis 0 comma 0 right parenthesis. Function B is also a concave up parabola, and passes through left parenthesis negative 4 comma 4.5 right parenthesis, left parenthesis negative 2 comma 2 right parenthesis, left parenthesis 0 comma 0.5 right parenthesis, left parenthesis 2 comma 0 right parenthesis, and left parenthesis 4 comma 0.5 right parenthesis. The 2 curves intersect at left parenthesis negative 1.1 comma 1.1 right parenthesis and at left parenthesis 0.5 comma 0.25 right parenthesis. Values are approximate.

Describe the transformations from Function A
to Function B
.

(1 point)

wider and shifted left 2 units

narrower and shifted right 2 units

narrower and shifted left 2 units

wider and shifted right 2 units

Answer 1

Function A is f(x)=x^2. Function B fits g(x)=a(x−2)^2 with vertex at (2,0); using g(0)=0.5 gives a(4)=0.5 ⇒ a=1/8, so g(x)=(1/8)(x−2)^2. Thus B is a horizontal shift right 2 units and a vertical shrink (wider) compared to A.

Answer: wider and shifted right 2 units.