Use the Rational Zero Test to list all possible rational zeros of $f(x)=4x^5-8x^4-5x^3+10x^2+x-2$. Verify that the zeros of f shown on the graph are continued in the list.

Graph each function. Compare the graph of each function with the graph of $y=x^2$.

(b) $g(x)=(3x)^2+1$

Graph each function. Compare the graph of each function with the graph of $y=x^2$.

(a) $f(x)=(x-1)^2$

Write the complex number in standard form.

$$-10i+i^2$$

One of the fundamental themes of calculus is to find the slope of the tangent line to a curve at a point. To see how this can be done, consider the point $(2,4)$ on the graph of the quadratic function $f(x)=x^2$.

(f) What can you conclude the slope of the tangent line at $(2,4)$ to be? Explain.

Identify any intercepts and asymptotes of the graph of the function. Then sketch a graph of the function.

$$f(x)=\frac{2x^2-5x-12}{x^2-16}$$

One of the fundamental themes of calculus is to find the slope of the tangent line to a curve at a point. To see how this can be done, consider the point $(2,4)$ on the graph of the quadratic function $f(x)=x^2$.

(e) Evaluate the slope formula from part d for $h=-1$, $1$, and $0.1$. Compare these values with those in parts a–c.

One of the fundamental themes of calculus is to find the slope of the tangent line to a curve at a point. To see how this can be done, consider the point $(2,4)$ on the graph of the quadratic function $f(x)=x^2$.

(d) Find the slope of the line joining $(2,4)$ and $(2+h,f(2+h))$ in terms of the nonzero number $h$.

Use long division to divide.

$14$. $(6x^3-16x^2+17x-6)\div(3x-2)$

One of the fundamental themes of calculus is to find the slope of the tangent line to a curve at a point. To see how this can be done, consider the point $(2,4)$ on the graph of the quadratic function $f(x)=x^2$.

(c ) Find the slope of the line joining $(2,4)$ and $(2.1,4.41)$. Is the slope of the tangent line at $(2,4)$ greater than or less than the slope of the line through $(2,4)$ and $(2.1,4.41)$?

Graph each function. Compare the graph of each function with the graph of $y=x^2$.

(d) $k(x)=x^2-3$

Graphical Reasoning The graph of one of the following functions is shown below. Identify the function shown in the graph. Explain why each of the others is not the correct function. Use a graphing utility to verify your result.

d) $k(x)=(x+1)(x+2)(x-3.5)$

One of the fundamental themes of calculus is to find the slope of the tangent line to a curve at a point. To see how this can be done, consider the point $(2,4)$ on the graph of the quadratic function $f(x)=x^2$.

(b) Find the slope of the line joining $(2,4)$ and $(1,1)$. Is the slope of the tangent line at $(2,4)$ greater than or less than the slope of the line through $(2,4)$ and $(1,1)$?

Graph each function. Compare the graph of each function with the graph of $y=x^2$.

(c ) $h(x)=x^2+3$