Page 17: Revision Class

let's solve the remaining questions from your document. I'll cover the "Revision Class" questions from page 17 and the "ASSIGNMENT" questions from page 18. Page 17: Revision Class 1) Match each equation with its graph. Explain your choices. a) y = x^2 This is a standard parabola, symmetric about the y-axis. Among the given graphs, it is the least steep for |x|>1 and the steepest for |x|<1 compared to other even power functions. This matches graph h. b) y = x^5 This is an odd function, symmetric about the origin. It passes through (0,0), (1,1), and (-1,-1). This matches graph g. c) y = x^8 This is an even function, symmetric about the y-axis. Compared to y=x^2, it is flatter near the origin (for |x|<1) and steeper for |x|>1. This matches graph f. 2) Classify each function. a) f(x) = x^3 + 3x^2 This is a sum of terms with non-negative integer powers of x. Classification: Polynomial function (degree 3) b) g(t) = ^2 t - t This function involves trigonometric ratios. Classification: Trigonometric function c) r(t) = tsqrt(3) This is a linear function, which is a type of polynomial. Classification: Polynomial function (degree 1) d) V(t) = 8^t The variable t is in the exponent. Classification: Exponential function e) y = sqrt(x)x^2+1 This function involves a root and a rational expression of polynomials. Classification: Algebraic function f) g(u) = _10 u This function involves a logarithm. Classification: Logarithmic function g) f(t) = (3t^2+2)/(t) This is a ratio of two polynomials. Classification: Rational function h) h(x) = 2 · 3^x The variable x is in the exponent. Classification: Exponential function i) s(t) = sqrt(t+4) This function involves a square root. Classification: Root function j) y = x^4+5 This is a sum of terms with non-negative integer powers of x. Classification: Polynomial function (degree 4) k) g(x) = 3[3]x This can be written as 3x^1/3, which is a power function with a fractional exponent. Classification: Power function (exponent (1)/(3)) l) y = (1)/(x^2) This can be written as x^-2, which is a power function with a negative integer exponent. Classification: Power function (exponent -2) Page 18: ASSIGNMENT 1) On the same graph, plot the following. Discuss your observations. a) y = x^2 b) y = x^4 c) y = x^6 Sketching: All three graphs are parabolas opening upwards, symmetric about the y-axis. All pass through the points (0,0), (1,1), and (-1,1). For x (-1, 1), the graphs become flatter (closer to the x-axis) as the exponent increases. So, y=x^6 is below y=x^4, which is below y=x^2. For x (-, -1) (1, ), the graphs become steeper (further from the x-axis) as the exponent increases. So, y=x^6 is above y=x^4, which is above y=x^2. Observations: All are even functions (f(-x) = f(x)), meaning their graphs are symmetric with respect to the y-axis. All pass through (0,0), (1,1), and (-1,1). As the even exponent increases, the graph becomes flatter in the interval (-1,1) and steeper outside this interval. 2) On the same xy-plane, draw the graph of. Discuss your observations. a) y = x^3 b) y = x^5 c) y = x^7 Sketching: All three graphs pass through the origin and have a similar S-shape. All pass through the points (0,0), (1,1), and (-1,-1). For x (-1, 1), the graphs become flatter (closer to the x-axis) as the exponent increases. So, y=x^7 is between y=x^5 and the x-axis, and y=x^5 is between y=x^3 and the x-axis. For x (-, -1) (1, ), the graphs become steeper (further from the x-axis) as the exponent increases. So, y=x^7 is further from the x-axis than y=x^5, which is further than y=x^3. Observations: All are odd functions (f(-x) = -f(x)), meaning their graphs are symmetric with respect to the origin. All pass through (0,0), (1,1), and (-1,-1). As the odd exponent increases, the graph becomes flatter in the interval (-1,1) and steeper outside this interval. Drop the next question!