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Transformations of functions worksheets Grade 10

Write the new function after shifts, reflections and stretches.

The front of the free transformations of functions worksheet
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Free · Worked example · 13 problems · Answer key · US Letter

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How to do it

Right h: replace x with (x − h). Left h: replace x with (x + h). Up k: add k. Reflect over the x-axis: multiply by −1. Stretch by a: multiply by a.

f(x)=∣x∣;reflect, stretch by 2, left 4, up 1→g(x)=−2∣x+4∣+1f(x) = |x|;\quad \text{reflect, stretch by }2,\ \text{left }4,\ \text{up }1\quad \to \quad g(x) = -2|x + 4| + 1
left 4:x becomes (x+4)\text{left }4: x\ \text{becomes }(x + 4)
reflect and stretch: multiply by −2\text{reflect and stretch: multiply by }-2
up 1: add 1\text{up }1:\ \text{add }1
g(x)=−2∣x+4∣+1g(x) = -2|x + 4| + 1

Example problems

  1. f(x)=∣x∣;left 5, down 7→f(x) = |x|;\quad \text{left }5,\ \text{down }7\quad \to \quad
  2. f(x)=x2;left 6, up 6→f(x) = x^{2};\quad \text{left }6,\ \text{up }6\quad \to \quad
  3. f(x)=∣x∣;right 1, up 2→f(x) = |x|;\quad \text{right }1,\ \text{up }2\quad \to \quad
  4. f(x)=x3;stretch by 3, left 2, up 9→f(x) = x^{3};\quad \text{stretch by }3,\ \text{left }2,\ \text{up }9\quad \to \quad

Functions

  1. Evaluating functions
  2. Finding the domain of a function
  3. Adding, subtracting and multiplying functions
  4. Composition of functions
  5. Inverse functions
  6. Transformations of functions
  7. Even and odd functions
  8. Average rate of change