1.4 - 1.6 AP Pre-Calculus Quiz

The sign of the leading term of $p$ is positive, and the degree of the leading term of $p$ is even; therefore, $\lim_{x \to -\infty} p(x) = \infty$ and $\lim_{x \to \infty} p(x) = \infty$.

The sign of the leading term of $p$ is negative, and the degree of the leading term of $p$ is odd; therefore, $\lim_{x \to -\infty} p(x) = \infty$ and $\lim_{x \to \infty} p(x) = -\infty$.

The sign of the leading term of $p$ is positive, and the degree of the leading term of $p$ is odd; therefore, $\lim_{x \to -\infty} p(x) = -\infty$ and $\lim_{x \to \infty} p(x) = \infty$.

The sign of the leading term of $p$ is negative, and the degree of the leading term of $p$ is odd; therefore, $\lim_{x \to -\infty} p(x) = -\infty$ and $\lim_{x \to \infty} p(x) = \infty$.

$p(-3) = 4$ is a relative maximum.

$p(-3) = -4$ is a relative maximum.

$p(-3) = 4$ is a relative minimum.

$p(-3) = -4$ is a relative minimum.

$0.25(x - 5)(x - 1)(x + 8)$

$0.25(x + 5)(x + 1)(x - 8)$

$0.25(x - 5)^{2}(x - 1)(x + 8)$

$0.25(x + 5)^{2}(x + 1)(x - 8)$

The function $f$ has a local minimum at $(-1, -36)$.

The function $f$ has a local minimum at $(5, 0)$.

The function $f$ has a local maximum at $(3, 4)$.

The function $f$ has a local maximum at $(1, 0)$.

$p$ has exactly two distinct real zeros.

$p$ has exactly three distinct real zeros.

$p$ has exactly one distinct real zero and no non-real zeros.

$p$ has exactly one distinct real zero and two non-real zeros.

3

4

5

6

$-3x^2 + 4x^2 + 1$

$-x^4 + 2x^3 + 6$

$2x^3 - 7x^2 + 4x$

$4x^6 + x^3 - 5$

$g$ is an even function for all real $k$, and $\lim_{x \to \pm\infty} g(x) = +\infty$.

$g$ is an odd function only if $k = 0$, and $\lim_{x \to -\infty} g(x) = -\infty$.

$g$ is neither even nor odd for $k \ne 0$, but $\lim_{x \to -\infty} g(x) = +\infty$.

$g$ is odd for $k \ne 0$, but its end behavior depends on $k$.

One

Three

Four

Five