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Calculus 4E-Ch 16
Calculus 4E - Ch 16: Graphs & Slopes
| Question | Answer |
|---|---|
| Analytic geometry was developed in the early to mid-1600s and combines | numbers with shapes using the Cartesian coordinate system. |
| A point on a graph is a ___________________ object, and multiple points can be combined to create other _____________________ shapes. | geometrical; geometrical |
| Since the numerical points have "addresses" on Cartesian coordinates, the Cartesian coordinate system unites the two fundamental mathematical realms of ___________________ and ____________________. | numbers (and) points |
| The formula y = 2x+1 refers to an infinite number of points because it describes a ______________, which is inherently an infinite number of points. | line |
| In the formula y = mx + b, the "m" stands for | the slope of the line. |
| In the formula y = mx + b, the "b" stands for | the y-intercept, where the line crosses or INTERSECTS the y-axis. |
| Geometrically, the derivative of a function is the _____________ of that function. | slope |
| Geometrically, the shape of the function y(x) = x^2 is a | parabola. |
| The four types of values that a slope can take are: | negative, zero, positive, or undefined. |
| A _________________ slope, when read from left to right, slopes DOWNWARD. | negative |
| A _________________ slope, when read from left to right, slopes UPWARD. | positive |
| A _________________ slope does not slope at all; it is a HORIZONTAL line. | zero |
| An ________________________ slope is infinitely steep; it is a VERTICAL line. | undefined |
| A _________________ line, meaning "to cut", is a line connecting two points on a parabola. | secant |
| The curve on a parabola is constantly __________________, so we talk about its slopeS (plural). | changing |
| A _________________ line is a line that touches a curve at only one point. | tangent |
| The steepness of a line that's tangent to a point on a ________________ shows the steepness (or slope) of the parabola AT that point. | parabola |
| It doesn't make sense to talk about secant lines or tangent lines of a strait line because there _______ ______secant lines or tangent lines of a strait line | are no |
| In terms of delta notation, the SLOPE of the SECANT line is | Δy/Δx |
| The DERIVATIVE of y(x) is the limit of the SLOPE of the ____________ line as it approaches the SLOPE of the _____________ line. | secant; tangent |
| A graph is a ______________ of a function. | picture |
| A _________________ is a sentence about a function. | formula |
| A simple definition of slope: | "rise over run." |
Created by:
MrsHough
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