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Lesson 1: Graphing Square Root Functions — Practice Questions

  1. 1. How is the graph of $g(x) = \sqrt{x} - 5$ obtained from the parent function $f(x) = \sqrt{x}$?

    • A. Shifted up 5 units
    • B. Shifted down 5 units
    • C. Shifted left 5 units
    • D. Shifted right 5 units
  2. 2. The graph of $y = \sqrt{x}$ is shifted vertically down by 7 units. If the new function is written as $y = \sqrt{x} + k$, what is the value of $k$? The value of $k$ is ___.

  3. 3. Which function represents the graph of $f(x) = \sqrt{x}$ after a vertical shift up by 4 units?

    • A. $g(x) = \sqrt{x} - 4$
    • B. $g(x) = \sqrt{x+4}$
    • C. $g(x) = \sqrt{x} + 4$
    • D. $g(x) = 4\sqrt{x}$
  4. 4. The graph of the parent function $f(x) = \sqrt{x}$ starts at the point $(0, 0)$. What is the starting point of the graph of $g(x) = \sqrt{x} - 6$? The starting point is (___, ___).

  5. 5. Consider the function $h(x) = \sqrt{x} + 10$. How does its graph compare to the parent function $f(x) = \sqrt{x}$?

    • A. It is shifted 10 units down.
    • B. It is shifted 10 units up.
    • C. It is shifted 10 units right.
    • D. It is shifted 10 units left.
  6. 6. For the function $G(x) = \sqrt{5x - 1}$, find $G(2)$.

    • A. 3
    • B. 4
    • C. $\sqrt{10}$
    • D. not a real number
  7. 7. For the function $f(x) = \sqrt[4]{3x^3}$, find $f(3)$. The value is ___.

  8. 8. For the function $F(x) = \sqrt{3 - 2x}$, find $F(-11)$. The value is ___.

  9. 9. For the function $g(x) = \sqrt[4]{4 - 4x}$, find $g(1)$. The value is ___.

  10. 10. For the function $F(x) = \sqrt{8 - 4x}$, find $F(1)$.

    • A. 2
    • B. 4
    • C. 1
    • D. not a real number