1. )Solve the equation.
x+2−−−−√+2=2x+3−−−−−√
Drag the choice or choices into the box to correctly state the solution to the equation.
Solution to x+2−−−−√+2=2x+3−−−−−√
x=−23
x=−1
x=1
x=23
2.) What is the graph of the function?
f(x)=−1x−3+2
Rational function on the coordinate plane. The curve has two branches. The left branch lies in the second quadrant. This branch passes through negative 4 comma 7 over 2 and negative 3 comma 4. The right branch begins in the third quadrant, increases into the second quadrant, and then into the first quadrant. This branch passes through 0 comma 5 over 2 and 1 comma 8 over 3.
Rational function on the coordinate plane. The curve has two branches. The left branch begins in the second quadrant and increases into the first quadrant. This branch passes through 0 comma 7 over 2 and 1 comma 4. The right branch begins in the fourth quadrant and increases into the first quadrant. This branch passes through 3 comma 2 and 4 comma 5 over 2.
Rational function on the coordinate plane. The curve has two branches. The left branch begins in the second quadrant and increases into the first quadrant. This branch passes through 0 comma 7 over 3 and 2 comma 3. The right branch begins in the fourth quadrant and increases into the first quadrant. This branch passes through 4 comma 1 and 6 comma 5 over 3.
Rational function on the coordinate plane. The curve has two branches. The left branch lies in the second quadrant. This branch passes through negative 6 comma 7 over 3 and negative 4 comma 3. The right branch begins in the third quadrant, increases into the second quadrant, and then into the first quadrant. This branch passes through negative 2 comma 1 and 1 comma 7 over 4.
6.) What are the roots of the equation?
0=x4+x3+4x2+6x−12
Select all correct answers.
−6
−2
−1
1
2
6
i6√
−i6√
6√
−6√
7.) What is the equation of the slant asymptote of the rational function?
f(x)=10x3−15x2+x−15x2−2
y=x−3
y=2x−3
y=x−115
y=2x−115
3.) What is the end behavior of the polynomial function?
Drag the choices into the boxes to correctly describe the end behavior of the function.
f(x)=6x^9−6x^4−6 f(x)=−3x^4−6x+4x−5
As x→−∞
As x→∞
f(x)→∞ or f(x)→−∞
