# Tutor profile: Stephanie W.

## Questions

### Subject: Pre-Calculus

Find the domain and range of the following equation: x^2-4x-4

The domain is all real numbers or (-inf, inf). The range is all real numbers greater than or equal to -8 or [-8, inf)

### Subject: Basic Math

Adam is 7 years old. On her next birthday, his sister Fran will be twice as old as Adam is now. How old is Fran?

Fran is 13. Explanation: If Fran is nearly twice his age, we should figure out what that means. Adam is 7; twice that age is 14. If she is not yet 14, but will be on her next birthday, then she must be 13.

### Subject: Algebra

What information can you find from an equation in the form of y=mx+b, for example, y= 1/2 x+3?

The slope-intercept form of an equation is useful for graphing because it is simple to find both the slope, or steepness of the line, and y-intercept, the point where the line crosses the y-axis. In the formula y=mx+b, m represents the slope of the line and b represents the y-intercept. In the equation y=1/2x+3, the slope of the line is 1/2; this is a ratio of the "rise" to the "run". This is a positive value, indicating that the line has a positive, or upward, slope. The y-intercept of the line is 3 which means that the line crosses the y axis at the point (0,3). From these two pieces of information, you can graph this line. Start by plotting the point (0,3). Next from the point (0,3), use the slope to move up 1, and to the right 2 to plot your next point. Continue using the slope to plot more points if desired. Draw a line connecting the points that you graphed to illustrate the graph of the equation!

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