Polynomial and Rational Functions

By identifying discontinuities in the numerator only.

By observing where the graph crosses the y-axis.

By locating where the denominator equals zero only.

By finding values that make both numerator and denominator equal zero.

$\frac{ax+b}{(dx+c)^{m}x+k}+l$

$\frac{ax^{m}+b}{c(ax+b)}$

The expression could have been $\frac{(ax+b)^{n}}{(ax+b)^{n-1}(cx+d)}$

$\frac{a(cx+d)+b}{c(cx+d)^{n}}$

Incorrect answer 2.

Incorrect answer 3.

The locations of vertical asymptotes remain unchanged.

Incorrect answer 1.

$x^2 + 4$

$x - 2$

Cannot be simplified

$x + 2$

The factor (x-7) causes undefined behavior at x=-5.

The factor (x+5) cancels out.

The numerator has higher degree than the denominator.

There is a vertical asymptote at x=-5.

f(x) approaches 14.

There is no horizontal asymptote.

f(x) approaches -7.

f(x) approaches 8.

Replacing operation causes inversion about origin thereby altering initial condition respective towards symmetrical characteristics possessed through $r()$ afore mentioned adjustments take place.

Symmetry around origin gets induced irrespective whether such property existed prior manipulation done unto $R()$.

There won't be any change regarding symmetry aspects related directly with modification imposed upon $R(x)$.

The function becomes symmetric about y-axis if originally it was asymmetric, otherwise, symmetry is preserved.

30 items

20 items

15 items

25 items

An absolute maximum value on its entire domain.

Horizontal or slant asymptotes depending on degrees of polynomials in numerator and denominator.

Asymptotes along certain lines due to division by zero issues.

Discontinuities or "holes" when common factors are canceled out.

F(X) remains unchanged

F(X) approaches infinity

F(X) approaches negative infinity

F(X) becomes zero