Calculus Chapter 1 Exam Questions with Correct Grade A+ Solutions

Calculus Chapter 1 Exam Questions with Correct Grade A+ Solutions The Vertical Line Test - Correct Answers: 1. Draw a vertical line. 2. Does the intersect the function at more than one point? 3. No - This function is indeed a function. 4. Yes - This "function" is a fraud! Graphing a Function - Correct Answers: Use the Point-Slope Equation and the Slope-Intercept Equation. Use Slope ("m"). You might see perpendicular or parallell verifications. Point-Slope Equation - Correct Answers: y = m(x - x1) - y1 or y - y1 = m(x - x1) Where "m" is the slope of the line and (x1, y1) is a given point which is on the line. To graph the line, you can simply graph the given point and use the slope to determine a second point. Slope-Intercept Equation - Correct Answers: y = mx + b Where "m" is the slope, "b" is the y-intercept, and "x" and "y" follow the coordinate formula (x,y) The Common Functions: - Correct Answers: - Linear - Quadratic - Cubic - Square Root - Absolute Value - Rational - Logarithmic - Exponential Linear Function - Correct Answers: The highest power over the x-variable is 1 Quadratic Function - Correct Answers: The highest power over the x-variable(s) is 2 Cubic Function - Correct Answers: The highest power over the x-variable(s) is 3 Square Root Function - Correct Answers: The x-variable is square rooted Absolute Value Function - Correct Answers: The x-variable is within absolute value signs Rational Function - Correct Answers: The x-variable is in the denominator Logarithmic Function - Correct Answers: The "log" or "ln" of the x-variable is taken Exponential Function - Correct Answers: The x-variable is an exponent above a number Domains and Ranges - Correct Answers: - "x" = read from left to right - "y" = read from bottom to top The Number "e" - Correct Answers: e = 2.7182... Inverse Trig Functions - Correct Answers: sin ^ -1 = arcsin... Period for Sine - Correct Answers: 2 (pi) Period for Cosine - Correct Answers: 2 (pi) Period for Tangent - Correct Answers: pi Finding the Periods of Graphs - Correct Answers: y = a sin b x is 2(pi) / b Transformations of Trig Graphs - Correct Answers: y = a [ f (b (x = c)) ] + d Transformations Key: - Correct Answers: - a = vertical stretch or shrink; reflection about the x-axis - b = horizontal stretch or shrink; reflection about the y-axis - c = horizontal shift - d = vertical shift