# Chapter 1: Fundamentals

1.2. Exponents and Radicals

The speed of light is about 186,000 mi/s. Use the information in Exercise 88(a) to find how long it takes for a light ray from the sun to reach the earth.

Q1.

The imaginary number *i* has the property that ${i}^{2}=\_\_\_$.

Q1.

Explain in your own words what it means for an equation to model a real-world situation, and give an example.

Q1.

We find the “steepness.” Or slope, of a line passing through two points by dividing the difference in the__ __coordinates of these points by the difference in the coordinates__ __. So the line passes through the points (0,1) and (2,5) slope.

Q1.

Question: 1. Give an example of each of the following:

- A natural number
- An integer that is not a natural number
- A rational number that is not an integer
- An irrational number

Q1.

The point that is 3 units to the right of the *y*-axis and 5 units below the *x*-axis has coordinates$\left(\text{\_\_\_\_,\_\_\_}\right)$.

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(a) If $x<5,$ then $x-3\_\_\_\_\_\_\_\_\_\_2$.

(b) If $x\le 5,$ then $3x\_\_\_\_\_\_\_\_\_\_15$.

(c) If $x\ge 2,$ then $-3x\_\_\_\_\_\_\_\_\_\_-6$

(d)If $x<-2,$ then $-x\_\_\_\_\_\_\_\_\_\_2$.

Q1.

a. Using exponential notation, we can write the product$5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5$as ______ .

b, In the expression${3}^{4}$the number 3 is called the ______ , and the number 4 is called the _____ .

Q1.

Give an example of each of the following:

a. A natural number

b. An integer that is not a natural number

c. A rational number that is not an integer

d. An irrational number

Q1.

The solutions of the equation ${x}^{2}-2x-3=0$ are the _____-intercepts of the graph of$y={x}^{2}-2x-3$.