Curve Sketching (uppersixth science pure maths )

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Test your knowledge on rational function curves!

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Curve Sketching (uppersixth science pure maths )


Froggy Jumps Curve Sketching (uppersixth science pure maths )Online version Test your knowledge on rational function curves! by YAKILI LMS 1 What is the key feature of a rational function's graph? a Only straight lines b Parabolas and circles c Asymptotes and holes 2 What is a stationary point on a graph? a A point where the graph is maximum b A point where the derivative is zero c A point where the graph is minimum 3 What does a turning point indicate? a A point where the curve is flat b A change in the direction of the curve c A point of inflection 4 At a maximum point, the derivative is? a Zero or negative b Positive c Undefined 5 What is the second derivative test used for? a To classify stationary points as maxima or minima b To determine concavity c To find the slope 6 If the first derivative changes from positive to negative, the point is a? a Local maximum b Inflection point c Local minimum 7 What is an inflection point? a A point where the curve changes concavity b A maximum point c A minimum point 8 At a stationary point, the derivative equals? a Negative b One c Zero 9 Which of the following is true about stationary points? a They occur where the first derivative is zero b They are always maxima c They occur where the second derivative is zero 10 A point where the first derivative is zero but the second derivative is positive is a? a Point of inflection b Local maximum c Local minimum 11 What does the first derivative represent on a graph? a The area under the curve b The curvature c The slope of the tangent 12 What is an asymptote? a A line that the graph crosses b A line that a graph approaches but never touches c A point where the graph intersects 13 Which type of asymptote is a vertical line? a Horizontal asymptote b Vertical asymptote c Oblique asymptote 14 What does a horizontal asymptote represent? a The value the function approaches as x goes to infinity b The maximum point of the graph c Where the graph crosses the y-axis 15 Which asymptote is a slant or oblique line? a Vertical asymptote b Oblique asymptote c Horizontal asymptote 16 In rational functions, when does a vertical asymptote occur? a When the denominator equals zero b When the numerator is undefined c When the numerator equals zero 17 What is the main purpose of asymptotes in graphing? a To identify intercepts b To find the maximum points c To show the end behavior of the graph 18 Can a graph cross its asymptote? a No, never b Yes, except for vertical asymptotes c Only at the origin 19 What type of asymptote is approached as x approaches infinity? a Vertical asymptote b Horizontal asymptote c Oblique asymptote 20 What is the asymptote of the function y = 1/x? a x=1 b Both x=0 and y=0 c y=1 21 When does a rational function have an oblique asymptote? a When degrees are equal b When the degree of numerator is exactly one more than the denominator c When the numerator is zero 22 What must a rational function's denominator not be for asymptotes to exist? a Zero b One c Infinity 23 When does a vertical asymptote occur? a When the denominator is zero and numerator is not zero b When numerator is zero c When numerator and denominator are zero 24 What indicates a horizontal asymptote? a When numerator equals denominator b Behavior as x approaches zero c Behavior of the function as x approaches infinity 25 Can a function have both vertical and horizontal asymptotes? a No b Only vertical c Yes 26 What is a slant asymptote? a A horizontal line b A diagonal asymptote when degree of numerator is one more than denominator c A vertical line 27 When does an oblique asymptote occur? a When numerator degree is less b When numerator and denominator are equal c When numerator degree is exactly one higher than denominator 28 What is the key condition for a vertical asymptote at x=a? a Denominator zero at x=a, numerator not zero b Both numerator and denominator zero c Numerator zero at x=a 29 What does the end behavior of a function determine? a Horizontal asymptote b Vertical asymptote c Slant asymptote 30 Can a rational function have no asymptotes? a No, always has asymptotes b Yes, if it is a polynomial c Only if it is linear 31 What is the main condition for a horizontal asymptote at y=L? a Limit of the function as x approaches infinity is L b Function crosses y=L c Function is undefined at y=L 32 What is the degree of the numerator in a rational function? a It can be any degree, often less than or equal to the denominator. b Always higher than the denominator. c Always equal to the denominator. 33 What shape do the graphs of rational functions with quadratic denominators typically have? a Linear graphs. b Parabolic curves. c They often have hyperbolic shapes with asymptotes. 34 What is a vertical asymptote in a rational function? a A line where the function crosses the x-axis. b A line where the function approaches infinity, usually where the denominator is zero. c A horizontal line at y=0. 35 How do you find the horizontal asymptote of a rational function with quadratic denominator? a Set numerator to zero. b Compare degrees of numerator and denominator; if equal, divide leading coefficients. c Find where numerator equals denominator. 36 What indicates a hole in the graph of a rational function? a A common factor canceled out in numerator and denominator. b A vertical asymptote. c A point where the graph crosses the x-axis. 37 When sketching, what is important about the y-intercept? a It is the same as the x-intercept. b It is found by evaluating the function at x=0. c It is always at y=1. 38 What is the general behavior of the graph as x approaches infinity for these functions? a It diverges to infinity without asymptotes. b It always goes to zero. c It approaches the horizontal asymptote, if any. 39 How do you determine the x-intercepts of a rational function? a Set the numerator equal to zero and solve. b Set the denominator equal to zero. c Find where the function is undefined. 40 What is the significance of the quadratic in the denominator? a It influences the location of vertical asymptotes and the shape of the graph. b It has no effect on the graph. c It determines the x-intercepts. 41 Why are asymptotes important in sketching rational functions? a They are points where the graph crosses. b They show the behavior of the graph near undefined points or infinity. c They are irrelevant in graph sketching. 42 Which type of curve has no vertical asymptote? a An exponential function b A polynomial function c A rational function with a denominator zero 43 What is a key feature of polynomial functions? a They are always decreasing b They always have horizontal asymptotes c They have no vertical asymptotes 44 Which of these functions does not have a vertical asymptote? a f(x) = x^2 + 3 b f(x) = 1/x c f(x) = 1/(x-2) 45 Why do polynomial functions lack vertical asymptotes? a Because they are defined for all real x b Because they are exponential c Because they are periodic 46 Which function type always has a vertical asymptote? a Linear functions b Polynomial functions c Rational functions with zero denominator 47 What is the behavior of polynomial functions at infinity? a They tend to infinity or negative infinity b They oscillate c They approach a finite limit 48 Are exponential functions likely to have vertical asymptotes? a Only if they have a base less than 1 b Yes, always c No, they generally do not 49 Which of these has no vertical asymptote? a f(x) = 1/x b f(x) = 1/(x-1) c f(x) = 5x + 2 50 What is the main reason polynomial functions do not have vertical asymptotes? a They are continuous everywhere b They are discontinuous c They have holes

Curve Sketching (uppersixth science pure maths )

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Curve Sketching (uppersixth science pure maths )Online version

by YAKILI LMS

What is the key feature of a rational function's graph?

What is a stationary point on a graph?

What does a turning point indicate?

At a maximum point, the derivative is?

What is the second derivative test used for?

If the first derivative changes from positive to negative, the point is a?

What is an inflection point?

At a stationary point, the derivative equals?

Which of the following is true about stationary points?

A point where the first derivative is zero but the second derivative is positive is a?

What does the first derivative represent on a graph?

What is an asymptote?

Which type of asymptote is a vertical line?

What does a horizontal asymptote represent?

Which asymptote is a slant or oblique line?

In rational functions, when does a vertical asymptote occur?

What is the main purpose of asymptotes in graphing?

Can a graph cross its asymptote?

What type of asymptote is approached as x approaches infinity?

What is the asymptote of the function y = 1/x?

When does a rational function have an oblique asymptote?

What must a rational function's denominator not be for asymptotes to exist?

When does a vertical asymptote occur?

What indicates a horizontal asymptote?

Can a function have both vertical and horizontal asymptotes?

What is a slant asymptote?

When does an oblique asymptote occur?

What is the key condition for a vertical asymptote at x=a?

What does the end behavior of a function determine?

Can a rational function have no asymptotes?

What is the main condition for a horizontal asymptote at y=L?

What is the degree of the numerator in a rational function?

What shape do the graphs of rational functions with quadratic denominators typically have?

What is a vertical asymptote in a rational function?

How do you find the horizontal asymptote of a rational function with quadratic denominator?

What indicates a hole in the graph of a rational function?

When sketching, what is important about the y-intercept?

What is the general behavior of the graph as x approaches infinity for these functions?

How do you determine the x-intercepts of a rational function?

What is the significance of the quadratic in the denominator?

Why are asymptotes important in sketching rational functions?

Which type of curve has no vertical asymptote?

What is a key feature of polynomial functions?

Which of these functions does not have a vertical asymptote?

Why do polynomial functions lack vertical asymptotes?

Which function type always has a vertical asymptote?

What is the behavior of polynomial functions at infinity?

Are exponential functions likely to have vertical asymptotes?

Which of these has no vertical asymptote?

What is the main reason polynomial functions do not have vertical asymptotes?