This worksheet focuses on radical functions and algebraic operations. It covers key concepts such as identifying function equations from graphs, describing transformations like horizontal and vertical shifts and reflections, and performing operations including addition, multiplication, and composition of functions. The exercises are designed to strengthen the understanding of how changes in square root equations affect their graphical representation.
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اختبار شهادة تدريبي مؤقت للصف والمادة والفصل نفسه.
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
The graph shows a square root function with a starting point at (4, -2). This indicates a horizontal shift of 4 units to the \right, represented by (x - 4) inside the radical, and a vertical shift of 2 units down, represented by -2 outside the radical.
Question 2
DB ID: 1347
Points: 1
Which of these equations shifts a radical equation right 5 times and down once?
Explanation
A shift of 5 units to the \right is achieved by subtracting 5 from x inside the radical function, i.e., \(\sqrt{x - 5}\). A shift of 1 unit down is achieved by subtracting 1 from the entire function, resulting in \(y = \sqrt{x - 5} - 1\).
Question 3
DB ID: 1348
Points: 1
Which of these equations shifts a radical equation left 3 times?
Explanation
A horizontal shift of 3 units to the \left is represented by adding 3 to the variable x within the function's argument, resulting in \(y = \sqrt{x + 3}\).
Question 4
DB ID: 1349
Points: 1
What function best describes this graph?
Explanation
The graph starts at the point (0, -4), which indicates a vertical shift of 4 units down. Using the point (4, 0) on the graph, if we substitute x = 4 into \(y = 2\sqrt{4} - 4\), we get y = 2(2) - 4 = 0, which matches the graph.
Question 5
DB ID: 1350
Points: 1
\(f(x) = -\sqrt{x}\) Describe the transformation.
Explanation
A negative sign placed outside the radical function, as in \(f(x) = -\sqrt{x}\), results in a reflection of the parent function graph across the x-axis.
In function composition, evaluate the inner function first: g(5) = 5 - 2 = 3. Then substitute this result into the outer function: f(3) = 3(3) + 10 = 9 + 10 = 19.
Question 9
DB ID: 1354
Points: 1
g(x) = 3x + 4 and h(x) = 3x - 1. Find g(h(x)).
Explanation
To find g(h(x)), substitute the entire expression for h(x) into g(x) for x: g(3x - 1) = 3(3x - 1) + 4 = 9x - 3 + 4 = 9x + 1.
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