Curve sketching (Uppersixth Art Pure Maths )

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Test your knowledge on rational function curves!

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Curve sketching (Uppersixth Art Pure Maths )


Curve sketching (Uppersixth Art Pure Maths )Versión en línea Test your knowledge on rational function curves! por YAKILI LMS 1 A rational function can have horizontal asymptotes. Yes No 2 Rational functions are always continuous everywhere. Yes No 3 A stationary point always corresponds to a maximum. Yes No 4 At a stationary point, the slope of the tangent is horizontal. Yes No 5 Turning points only occur at the endpoints of a graph. Yes No 6 All stationary points are points of local maxima. Yes No 7 A turning point can be a maximum or a minimum. Yes No 8 A stationary point cannot be a point of inflection. Yes No 9 Stationary points are only found in quadratic functions. Yes No 10 A local maximum occurs where the function changes from increasing to decreasing. Yes No 11 A point of inflection is always a stationary point. Yes No 12 Vertical asymptotes occur where the denominator equals zero and the numerator does not. Yes No 13 A quadratic denominator guarantees the graph will have exactly two vertical asymptotes. Yes No 14 Quadratic denominators never produce holes in the graph. Yes No 15 The degree of the numerator determines the end behavior when it is higher than the denominator. Yes No 16 Rational functions are always symmetric about the y-axis. Yes No 17 Quadratic denominators can produce two vertical asymptotes if they factor into linear terms. Yes No 18 Sketching rational functions involves analyzing asymptotes and intercepts. Yes No 19 All rational functions with quadratic denominators have a constant asymptote. Yes No 20 A rational function with a quadratic denominator can have vertical asymptotes. Yes No 21 The numerator's degree must be less than the denominator's degree for the function to be defined everywhere. Yes No 22 The degree of the numerator has no effect on the end behavior of the graph. Yes No 23 Rational functions with quadratic denominators cannot have horizontal asymptotes. Yes No 24 The graph of a rational function can have holes if factors cancel out. Yes No 25 The graph of a rational function with a quadratic denominator is always a hyperbola. Yes No 26 The shape of the graph depends on the degree and coefficients of numerator and denominator. Yes No 27 Quadratic denominators do not influence the shape of the rational function's graph. Yes No 28 A quadratic denominator can create a vertical asymptote where it equals zero. Yes No 29 The degree of the numerator and denominator affects the end behavior of the graph. Yes No 30 A quadratic denominator always results in a parabola when graphed. Yes No 31 A horizontal line is a simple example of a curve without a vertical asymptote. Yes No 32 Logarithmic functions such as y = log(x) do not have vertical asymptotes. Yes No 33 The graph of y = x^2 has no vertical asymptote. Yes No 34 The graph of y = tan(x) has no vertical asymptote. Yes No 35 The graph of y = 1/x has no vertical asymptote. Yes No 36 Exponential functions like y = e^x have vertical asymptotes. Yes No 37 The line y = 5 is a horizontal line with no vertical asymptote. Yes No 38 The graph of y = 1/x^2 has no vertical asymptote. Yes No 39 A parabola does not have a vertical asymptote. Yes No 40 The curve y = 1/(x^2 - 4) has no vertical asymptote. Yes No 41 In inequalities of the form (ax + b) / (cx + d) > k, the sign of the denominator affects the solution set. Yes No 42 The inequality (3x + 2) / (2x - 4) > 1 is always true for all real x. Yes No 43 Inequalities of the form (ax + b) / (cx + d) > k can be solved by cross-multiplying without considering the sign of the denominator. Yes No 44 To solve inequalities like (ax + b) / (cx + d) > k, you often find a common denominator. Yes No 45 When solving (ax + b) / (cx + d) > k, the solution set always includes all real numbers. Yes No 46 An inequality of the form (ax + b) / (cx + d) > k involves a rational expression. Yes No 47 In the inequality (x - 1) / (x + 3) > 2, the critical points are x = 1 and x = -3. Yes No 48 The inequality (2x + 3) / (x - 1) > 4 is an example of a rational inequality. Yes No 49 The inequality (x + 2) / (x - 5) > 0 is true for x > 5 only. Yes No 50 The inequality (x + 5) / (x - 2) > 3 can be solved by considering the critical points where numerator or denominator equals zero. Yes No

Curve sketching (Uppersixth Art Pure Maths )

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Curve sketching (Uppersixth Art Pure Maths )Versión en línea

por YAKILI LMS

A rational function can have horizontal asymptotes.

Rational functions are always continuous everywhere.

A stationary point always corresponds to a maximum.

At a stationary point, the slope of the tangent is horizontal.

Turning points only occur at the endpoints of a graph.

All stationary points are points of local maxima.

A turning point can be a maximum or a minimum.

A stationary point cannot be a point of inflection.

Stationary points are only found in quadratic functions.

A local maximum occurs where the function changes from increasing to decreasing.

A point of inflection is always a stationary point.

Vertical asymptotes occur where the denominator equals zero and the numerator does not.

A quadratic denominator guarantees the graph will have exactly two vertical asymptotes.

Quadratic denominators never produce holes in the graph.

The degree of the numerator determines the end behavior when it is higher than the denominator.

Rational functions are always symmetric about the y-axis.

Quadratic denominators can produce two vertical asymptotes if they factor into linear terms.

Sketching rational functions involves analyzing asymptotes and intercepts.

All rational functions with quadratic denominators have a constant asymptote.

A rational function with a quadratic denominator can have vertical asymptotes.

The numerator's degree must be less than the denominator's degree for the function to be defined everywhere.

The degree of the numerator has no effect on the end behavior of the graph.

Rational functions with quadratic denominators cannot have horizontal asymptotes.

The graph of a rational function can have holes if factors cancel out.

The graph of a rational function with a quadratic denominator is always a hyperbola.

The shape of the graph depends on the degree and coefficients of numerator and denominator.

Quadratic denominators do not influence the shape of the rational function's graph.

A quadratic denominator can create a vertical asymptote where it equals zero.

The degree of the numerator and denominator affects the end behavior of the graph.

A quadratic denominator always results in a parabola when graphed.

A horizontal line is a simple example of a curve without a vertical asymptote.

Logarithmic functions such as y = log(x) do not have vertical asymptotes.

The graph of y = x^2 has no vertical asymptote.

The graph of y = tan(x) has no vertical asymptote.

The graph of y = 1/x has no vertical asymptote.

Exponential functions like y = e^x have vertical asymptotes.

The line y = 5 is a horizontal line with no vertical asymptote.

The graph of y = 1/x^2 has no vertical asymptote.

A parabola does not have a vertical asymptote.

The curve y = 1/(x^2 - 4) has no vertical asymptote.

In inequalities of the form (ax + b) / (cx + d) > k, the sign of the denominator affects the solution set.

The inequality (3x + 2) / (2x - 4) > 1 is always true for all real x.

Inequalities of the form (ax + b) / (cx + d) > k can be solved by cross-multiplying without considering the sign of the denominator.

To solve inequalities like (ax + b) / (cx + d) > k, you often find a common denominator.

When solving (ax + b) / (cx + d) > k, the solution set always includes all real numbers.

An inequality of the form (ax + b) / (cx + d) > k involves a rational expression.

In the inequality (x - 1) / (x + 3) > 2, the critical points are x = 1 and x = -3.

The inequality (2x + 3) / (x - 1) > 4 is an example of a rational inequality.

The inequality (x + 2) / (x - 5) > 0 is true for x > 5 only.

The inequality (x + 5) / (x - 2) > 3 can be solved by considering the critical points where numerator or denominator equals zero.