Question 1

Graph $y=f(x)$ by hand.
(a) $f(x)=|x+2|-1$
(b) $f(x)=\sqrt[3]{-x}$

Accepted Answer

The answer of Graph $y=f(x)$ by hand.
(a) $f(x)=|x+2|-1$
(b) $f(x)=\sqrt[3]{-x}$...

Question 2

Consider the piecewise-defined function defined by $f(x)=\left\{\begin{array}{ll}x^{2}-6 & \text { if } x \leq 1 \ \sqrt{x} & \text { if } x>1\end{array}\right.$.
(a) Graph $f$ by hand.
(b) Use a graphing calculator to obtain an accurate graph in the window $[-5,10]$ by $[-10,10]$.

Accepted Answer

The answer of Consider the piecewise-defined function defined by \(f(x)=\left\{\begin{array}{ll}x^{2}-6...

Question 3

If the point $(-1,-2)$ lies on the graph of $y=f(x)$, determine a point on the graph of each equation.
(a) $y=-f(x)$
(b) $y=f(-x)$

Accepted Answer

The answer of If the point $(-1,-2)$ lies on the...

Question 4

Given $f(x)=3 x^{2}-2 x-6$ and $g(x)=3 x+5$, find each of the following. Simplify the expression when possible.
(a) $(f-g)(x)$
(b) $\frac{f}{g}(x)$
(c) the domain of $\frac{f}{g}$
(d) $(f \circ g)(x)$
(e) $\frac{f(x+h)-f(x)}{h}(h \neq 0)$

Accepted Answer

(a) @#LAT-DLM&
(b) @#LAT-DLM&

Graph $y=f(x)$ by hand. (a) $f(x)=|x+2|-1$ (b) $f(x)=\sqrt[3]{-x}$

Consider the piecewise-defined function defined by $f(x)=\left\{\begin{array}{ll}x^{2}-6 & \text { if } x \leq 1 \\ \sqrt{x} & \text { if } x>1\end{array}\right.$ . (a) Graph $f$ by hand. (b) Use a graphing calculator to obtain an accurate graph in the window $[-5,10]$ by $[-10,10]$ .

If the point $(-1,-2)$ lies on the graph of $y=f(x)$ , determine a point on the graph of each equation. (a) $y=-f(x)$ (b) $y=f(-x)$

Given $f(x)=3 x^{2}-2 x-6$ and $g(x)=3 x+5$ , find each of the following. Simplify the expression when possible. (a) $(f-g)(x)$ (b) $\frac{f}{g}(x)$ (c) the domain of $\frac{f}{g}$ (d) $(f \circ g)(x)$ (e) $\frac{f(x+h)-f(x)}{h}(h \neq 0)$

Linear Functions, Equations, and Inequalities

Polynomial Functions

Rational, Power, and Root Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Analytic Geometry and Nonlinear Systems

The Unit Circle and Functions of Trigonometry

Trigonometric Identities and Equations

Applications of Trigonometry and Vectors

Further Topics in Algebra

Limits, Derivatives, and Definite Integrals

Reference: Basic Algebraic Concepts

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Exam 2: Analysis of Graphs of Functions

Graph y=f(x)y=f(x)y=f(x) by hand. (a) f(x)=∣x+2∣−1f(x)=|x+2|-1f(x)=∣x+2∣−1 (b) f(x)=−x3f(x)=\sqrt[3]{-x}f(x)=3−x​

If the point (−1,−2)(-1,-2)(−1,−2) lies on the graph of y=f(x)y=f(x)y=f(x) , determine a point on the graph of each equation. (a) y=−f(x)y=-f(x)y=−f(x) (b) y=f(−x)y=f(-x)y=f(−x)