Families of Radical Functions
Read this topicProblems 11
- An unknown radical function passes through the points (3,0)(3, 0)(3,0), (4,1)(4, 1)(4,1), and (11,2)(11, 2)(11,2). The function has not been vertically shifted or stretched. Whi…
- Let nnn be an integer. Which condition must hold for f(x)=xnf(x) = \sqrt[n]{x}f(x)=nx to be defined for negative values of xxx?
- Is it possible, using transformations (translation, rotation, stretching, etc.), to turn f(x)=x3f(x) = \sqrt[3]{x}f(x)=3x into g(x)=xg(x) = \sqrt{x}g(x)=x?
- True or False\text{True or False}True or False === The function f(x)=310x23+1f(x)=\frac3{10}x^{\frac23}+1f(x)=103x32+1 is graphed above.
- Which of the following equation's graphs can be obtained by vertically compressing the graph of y=xy = \sqrt{x}y=x by a factor of 13\frac{1}{3}31?
- If you shift the graph y=xy=\sqrt{x}y=x left by 222 units and then stretch the resulting graph to 3 times its vertical size, what is the new equation of the graph?
- If you shift the graph y=xy=\sqrt{x}y=x right by 555 units and then shrink the resulting graph to 12\frac{1}{2}21 its vertical size, what is the new equation of the graph?
- Start with the graph of y=xy = \sqrt{x}y=x in a 3×93\times 93×9 rectangular picture, ranging over x∈[0,9]x\in [0,9]x∈[0,9] and y∈[0,3]y\in [0,3]y∈[0,3]. Now suppose you used MS…
- yred=abx+5cy_{\text{red}} = a\sqrt{bx} + 5cyred=abx+5c Assume aaa, bbb, and ccc are positive, non-zero constants. If the red graph is only 3c3c3c above the blue one, what is t…
- ygreen=ax+cy_{\text{green}} = a\sqrt{x+c}ygreen=ax+c Assume aaa and ccc are positive, non-zero constants. If the green graph is only 2c2c2c to the left of the blue one, what i…
- The green graph (leftmost) is 333 units to the left of the blue graph (rightmost). If yblue=kxy_{\text{blue}} = \sqrt{kx}yblue=kx where kkk is some positive, non-zero constant…