Mathematics for IGCSE & O level - Sketching Curves (Section 5)

• 1

  How many x-intercepts does the graph of \(y = x^2 + 4\) have?

  Svar

  (A)

  0
• 2

  How many asymptotes does the graph of \(y = \frac{1}{x-2} + 3\) have?

  Svar

  (C)

  2
• 3

  Which of the following methods could be used to sketch a quadratic graph?

  Svar

  A

  B

  C
• 4

  In the equation \(y = \frac{a}{x}\), where does the graph not meet the axes?

  Svar

  (C)

  Both axes.
• 5

  Which value determines whether a parabola opens upwards or downwards?

  Svar

  (B)

  The sign of the coefficient of x^2
• 6

  Which of the following statements about the graph of \(y=x^3\) is correct?

  Svar

  (B)

  The graph passes through (0,0) and (1,1).
• 7

  When sketching a graph, which features are most important to include?

  Svar

  B

  C
• 8

  Which feature is essential to indicate on a graph?

  Svar

  A

  B
• 9

  Which of the following describes the behavior of \(y = \frac{1}{x}\) as \(x\) approaches infinity?

  Svar

  (C)

  y approaches 0
• 10

  What is the main purpose of sketching a graph?

  Svar

  (B)

  To visually represent the relationship between variables.
• 11

  What does 'a' determine in a graph of \(y = a^x\)?

  Svar

  (C)

  The base of the exponent, and growth/decay
• 12

  What happens when a positive constant is added to the entire equation of an exponential graph?

  Svar

  (B)

  Vertical translation up
• 13

  For a function of the form \(y = a^x\), what does the y-intercept always equal?

  Svar

  (B)

  1
• 14

  How many x-intercepts can a quadratic function have?

  Svar

  (A)

  0, 1, or 2
• 15

  In an exponential function \(y = a^x\), which factor affects the x-intercept?

  Svar

  (C)

  Neither
• 16

  What is a key feature of a reciprocal graph?

  Svar

  A

  C
• 17

  If you are sketching a graph, which of the following is the MOST important step?

  Svar

  (B)

  Drawing the correct shape for the type of graph.
• 18

  Which of the following can be determined by looking at a completed square form of a quadratic equation?

  Svar

  B

  C
• 19

  What happens to the graph of \(y = 2^x\) if the equation becomes \(y = 2^x - 4\)?

  Svar

  (C)

  The graph shifts 4 units downwards.
• 20

  If the function is \(y=x^3+x^2-6x\), how can you find where this graph crosses the x-axis?

  Svar

  (A)

  Set y = 0 and solve for x
• 21

  What is the equation of the line of symmetry for the graph of \(y = x^2 - 6x + 10\) after it has been rewritten in completed square form?

  Svar

  (B)

  x = 3
• 22

  Which of these options is correct about a quadratic function?

  Svar

  (B)

  A quadratic function forms a parabola.
• 23

  Which of the following statements is TRUE about the graph of an exponential function?

  Svar

  (B)

  It always passes through the point (0, 1).
• 24

  What is the main reason for rewriting a quadratic function in completed square form?

  Svar

  (C)

  To identify the vertex (turning point).
• 25

  What information is required to accurately sketch a linear graph?

  Svar

  (A)

  The slope and y-intercept