Algebra Practice Problems Quiz

Quiz 1 Practice Problems

• Problem 1: Given f(x) = 7x + d, find d if f(1) = 2 and the slope of a line perpendicular to f(x).
  • To find d, substitute x = 1 and f(1) = 2 into the equation: 2 = 7(1) + d. Solving for d, d = -5.
  • The slope of f(x) is 7.
  • The slope of a line perpendicular to f(x) is the negative reciprocal of 7, which is -1/7.

Problem 2

• Cricket Chirps and Temperature: The relationship between cricket chirps and temperature is linear.
  • 113 chirps at 70°F
  • 173 chirps at 80°F
  • Find the chirps per minute at 100°F
  • Calculate the rate of change (slope) in chirps per degree Fahrenheit by finding the difference in chirps over the difference in temperature: (173 - 113) / (80 - 70) = 6 chirps/degree.
  • Use the point-slope form to find the equation: y - y1 = m(x - x1), using the point (70, 113) and slope 6.
  • y = 6x + 513
  • Substitute the temperature of 100°F to the x in the above equation to get the chirps, y = 6*100 + 513= 1113

Problem 3: Composite Functions

• Given f(x) = sin x, g(x) = 5 – √x, and h(x) = x + 2.
  • Find the composite function (f ∘ g ∘ h)(x) and its domain.

Problem 4: Graph Transformations

• Given y = e^(x-1), write the equation that shifts the graph three units to the left.
  • Shifting the graph of y = e^(x-1) to the left by three units will change the equation to y = e^{(x - 1 + 3)} = e^{(x + 2)}.

Problem 5: Function Transformations

• Given a function f(x), describe the transformations when graphing f(-x) + 5.
  • The transformation f(-x) reflects the graph across the y-axis.
  • The transformation f(-x) + 5 shifts the graph vertically up by 5 units.