GCSEMathsEdexcelHigherFlashcards2. AlgebraFunctions

Functions (Edexcel GCSE Maths) Flashcards

Exam code: 1MA1

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Cards in this collection (16)

  • What is a function?

    A function is a combination of one or more mathematical operations that takes a set of numbers and changes them into another set of numbers.

  • What does the notation  straight f open parentheses x close parentheses equals...   indicate?

    The notation  straight f open parentheses x close parentheses equals...  indicates a function straight f, where x is the input and straight f open parentheses x close parentheses is the output.

  • What is the input of a function?

    The input of a function is the number being put into the function, often referred to as  x.

  • What is the output of a function?

    The output of a function is the number coming out of the function, often referred to as straight f open parentheses x close parentheses or y.

  • How would you find the value of straight f open parentheses 3 close parentheses for a function straight f open parentheses x close parentheses?

    To find the value of straight f open parentheses 3 close parentheses for a function straight f open parentheses x close parentheses, substitute x equals 3 into the equation of the function.

    For example, if straight f left parenthesis x right parenthesis equals 2 x plus 1, then straight f left parenthesis 3 right parenthesis equals 2 open parentheses 3 close parentheses plus 1 equals 6 plus 1 equals 7.

  • How would you find the value of x if you knew that straight f open parentheses x close parentheses equals 15?

    To find the value of x if you know that straight f open parentheses x close parentheses equals 15:

    • Set the equation for straight f open parentheses x close parentheses equal to 15

    • Then solve for x

    For example, if straight f open parentheses x close parentheses equals 2 x plus 1 and straight f open parentheses x close parentheses equals 15, then

    2 x plus 1 equals 15 space space space rightwards double arrow space space space 2 x equals 14 space space space rightwards double arrow space space space x equals 7

  • Define a composite function.

    A composite function is a function that 'combines' two functions.

    The output of one function is used as the input for the other function.

  • What does the notation fg open parentheses x close parentheses mean?

    fg open parentheses x close parentheses is the notation for a composite function made up of functions straight f and straight g.

    It means "straight f is applied to the output of straight g open parentheses x close parentheses".

    I.e., first put x into the function straight g, and next put the output straight g open parentheses x close parentheses into the function straight f.

    Note that the function on the right (straight g) acts first, and the function on the left (straight f) acts second.

  • What does the notation gf open parentheses x close parentheses mean?

    gf open parentheses x close parentheses is the notation for a composite function made up of functions straight g and straight f.

    It means "straight g is applied to the output of straight f open parentheses x close parentheses".

    I.e., first put x into the function straight f, and next put the output straight f open parentheses x close parentheses into the function straight g.

    Note that the function on the right (straight f) acts first, and the function on the left (straight g) acts second.

  • How would you find the value of fg open parentheses 2 close parentheses?

    To find the value of fg open parentheses 2 close parentheses:

    1. First substitute x equals 2 into the equation for straight g open parentheses x close parentheses.

    2. Then substitute the output straight g open parentheses 2 close parentheses into the equation for straight f open parentheses x close parentheses.

  • Give the definition of an inverse function.

    An inverse function is a function that does the exact opposite operations of the function it came from.

  • What is the notation for the inverse function of the function straight f open parentheses x close parentheses?

    The notation for the inverse function of the function straight f open parentheses x close parentheses is straight f to the power of negative 1 end exponent open parentheses x close parentheses.

  • What are the steps to find the inverse function straight f to the power of negative 1 end exponent open parentheses x close parentheses of straight f open parentheses x close parentheses?

    To find straight f to the power of negative 1 end exponent open parentheses x close parentheses:

    1. Write straight f open parentheses x close parentheses as y italic equals open parentheses formula space in italic space x close parentheses.

    2. Swap x and y to get x italic equals open parentheses formula space in italic space y close parentheses.

    3. Rearrange to make y the subject.

    4. Replace y with straight f to the power of negative 1 end exponent open parentheses x close parenthesesto rewrite as straight f to the power of negative 1 end exponent open parentheses x close parentheses equals....

  • If you knew that straight f open parentheses 3 close parentheses equals 10, how would you find straight f to the power of negative 1 end exponent open parentheses 10 close parentheses?

    An inverse function 'undoes' the operations of the original function.

    So if straight f turns 3 into 10, then straight f to the power of negative 1 end exponent turns 10 back into 3.

    I.e., if straight f open parentheses 3 close parentheses equals 10, then straight f to the power of negative 1 end exponent open parentheses 10 close parentheses equals 3.

  • What is ff to the power of negative 1 end exponent open parentheses x close parentheses equal to?

    ff to the power of negative 1 end exponent open parentheses x close parentheses is a composite function of straight f and its inverse straight f to the power of negative 1 end exponent.

    An inverse function 'undoes' the operations of the original function (and vice versa).

    So ff to the power of negative 1 end exponent open parentheses x close parentheses equals x.

    (Note that straight f to the power of negative 1 end exponent straight f open parentheses x close parentheses equals x as well.)

  • True or false?

    Completing the square can help find inverse functions.

    True.

    Completing the square can help rearrange a quadratic expression in order to find its inverse function.

Previous:Forming & Solving EquationsNext:Coordinate Geometry

    1. Number Operations

    2. Prime Factors, HCF & LCM

    3. Powers, Roots & Standard Form

    4. Fractions

    5. Percentages

    6. Simple & Compound Interest, Growth & Decay

    7. Fractions, Decimals & Percentages

    8. Rounding, Estimation & Bounds

    9. Surds

    10. Using a Calculator

    1. Introduction to Algebra

    2. Algebraic Roots & Indices

    3. Expanding Brackets

    4. Factorising

    5. Completing the Square

    6. Algebraic Fractions

    7. Rearranging Formulas

    8. Algebraic Proof

    9. Linear Equations

    10. Quadratic Equations

    11. Simultaneous Equations

    12. Iteration

    13. Forming & Solving Equations

    14. Functions

    15. Coordinate Geometry

    16. Linear Graphs

    17. Graphs of Functions

    18. Equation of a Circle

    19. Estimating Gradients & Areas under Graphs

    20. Real-Life Graphs

    21. Solving Inequalities

    22. Graphing Inequalities

    23. Transformations of Graphs

    24. Sequences

    1. Ratios

    2. Problem Solving with Ratios

    3. Direct & Inverse Proportion

    4. Standard & Compound Units

    5. Exchange Rates & Best Buys

    1. Symmetry & Shapes

    2. Angles in Polygons & Parallel Lines

    3. Bearings, Scale Drawing, Constructions & Loci

    4. Circle Theorems

    5. Area & Perimeter

    6. Circles, Arcs & Sectors

    7. Volume & Surface Area

    8. Congruence, Similarity & Geometrical Proof

    9. Area & Volume of Similar Shapes

    10. Pythagoras & Trigonometry

    11. Sine, Cosine Rule & Area of Triangles

    12. 3D Pythagoras & Trigonometry

    13. Vectors

    14. Transformations

    1. Introduction to Probability

    2. Simple Probability Diagrams

    3. Tree Diagrams

    4. Combined & Conditional Probability

    1. Averages, Ranges & Data

    2. Statistical Diagrams

    3. Histograms

    4. Cumulative Frequency & Box Plots

    5. Scatter Graphs & Correlation