Interactive multiple-choice quiz: اختبار الوحدة الثانية Linear and nonlinear functions ريفيل
اختبار الوحدة الثانية (Linear and nonlinear functions) مادة الرياضيات المتقدم ريفيل الصف التاسع الفصل الأول لعام 2026 - 2027. يتضمن الاختبار مراجعة شاملة لتمثيل المعادلات والمتباينات والمتابعات الحسابية. إحجز مكانك واستعد للامتحان بثقة كاملة.
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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.
Graph the following equation by using x- and y-intercepts: 5 - y = -3x
Explanation
The y-intercept is (0, 5) and the x-intercept is $(-\frac{5}{3}, 0)$. Graph C correctly shows the line passing through these points.
Question 2
2
Points: 1
Amanda has 210 in her school lunch account. She spends35 each week on school lunches. The equation y = 210 - 35x represents the total amount in Amanda's school lunch account y for x weeks of purchasing lunches. Graph the equation by using the intercepts.
Explanation
The y-intercept is (0, 210) and the x-intercept is (6, 0) because 35(6) = 210. Graph A is the correct representation.
Question 3
3
Points: 1
The graph shows the average ticket prices for the Miami Dolphins football team. The ticket prices have the greatest rate of change between _____?
Explanation
The rate of change between 2013 and 2014 is 71.14 - 65.16 = 5.98, which is the highest magnitude among the given intervals.
Question 4
4
Points: 1
Determine the slope of a line passing through the given points (-1, 8) and (7, 10). If the slope is undefined, write undefined. Write your answer as a decimal if necessary.
Find the value of r so that the line passing through (-3, r) and (7, -6) has a slope of $2\frac{2}{5}$.
Explanation
Slope $2\frac{2}{5} = \frac{12}{5}$. Using the formula: $\frac{12}{5} = \frac{-6 - r}{7 - (-3)} = \frac{-6 - r}{10}$. Cross multiplying gives 24 = -6 - r, so r = -30.
Question 6
6
Points: 1
What is the slope-intercept form of -16x - 4y = -56?
Explanation
Rearrange the equation: -4y = 16x - 56. Divide by -4: y = -4x + 14.
Question 7
7
Points: 1
Match the graph with its corresponding equation from the list below:
Explanation
The graph has a y-intercept of -4 and passes through (7, -1), which fits the equation $y = \frac{3}{7}x - 4$.
Question 8
8
Points: 1
Write an equation of a line in slope-intercept form with the given slope and y-intercept: slope: 3, y-intercept: 2
Explanation
The slope-intercept form is y = mx + b. Plugging in m=3 and b=2 gives y = 3x + 2.
Question 9
9
Points: 1
Write an equation in slope-intercept form for the graph shown.
Explanation
The graph has a y-intercept of 2 and a slope of $\frac{-4 - 2}{2 - 0} = -3$, so the equation is y = -3x + 2.
Question 10
10
Points: 1
Describe the translation in g(x) = x - 1 as it relates to the graph of the parent function. The graph of g(x) = x - 1 is a translation of the graph of the parent function 1 unit _____?
Explanation
Subtracting 1 from the function f(x) = x results in a vertical translation 1 unit downward.
Question 11
11
Points: 1
Jerome is buying paint for a mural. The total cost of the paint can be modeled by the function f(p) = 6.99p. He has a coupon for 5.95 off his purchase at the art supply store, so the final cost of his purchase can be modeled byg(p) = 6.99p - 5.95. Describe the translation ing(p)$ as it relates to f(p).
Explanation
Subtracting 5.95 from the function f(p) shifts the graph vertically downward by 5.95 units.
Question 12
12
Points: 1
Describe the transformation in g(x) = 6f(x) as it relates to the graph of the parent function. The graph of g(x) = 6f(x) is a _____ of the graph of the parent function.
Explanation
Multiplying the parent function by a factor greater than 1 (which is 6 in this case) results in a vertical stretch.
Question 13
13
Points: 1
Determine whether the sequence is an arithmetic sequence. Justify your reasoning: 82, 73, 64, 55, ...
Explanation
The difference between consecutive terms is constant (73-82 = -9, 64-73 = -9), so it is an arithmetic sequence.
Question 14
14
Points: 1
Determine the next three terms in the sequence: 31, 18, 5, ?, ?, ?
Explanation
The common difference is -13. So: 5 - 13 = -8, -8 - 13 = -21, and -21 - 13 = -34.
Question 15
15
Points: 1
Randi has been training for a marathon. At 1 mile, her time was 10 minutes and 30 seconds. At 2 miles, her time was 21 minutes. At 3 miles, her time was 31 minutes and 30 seconds. At 4 miles, her time was 42 minutes. Write a function to represent her sequence of data. Use n as the variable:
Explanation
10 minutes and 30 seconds is 10.5 minutes. The rate is 10.5 minutes per mile (21/2 = 10.5), so the function is f(n) = 10.5n.
Question 16
16
Points: 1
Graph the piecewise-defined function f(x) and state the domain and range: $f(x) = \begin{cases} -x + 1 & \text{if } x \leq -2 \\ -3x - 2 & \text{if } x > -2 \end{cases}$
Explanation
The function is defined for all x. For $x \leq -2$, $y \geq 3$. For x > -2, y can be any value less than 4. The union covers all real numbers.
Question 17
17
Points: 1
Graph the function $g(x) = -2\lfloor x \rfloor$ and state the domain and range.
Explanation
The floor function $\lfloor x \rfloor$ outputs integers. Multiplying these integers by -2 results in the set of all even integers.
Question 18
19
Points: 1
Certain types of glass heat and cool at a nearly constant rate when they are melted. Use the graph to determine the equation that represents this process: $y = ?|x - ?| + ?$
Explanation
The vertex of the absolute value graph is at (9, 1100) and it opens downwards. Using point (0, 29) to find the stretch factor results in -119.
Question 19
20
Points: 1
Use the graph of the function to write its equation.
Explanation
The graph is a standard absolute value function $f(x) = |x|$ shifted 1 unit down, placing the vertex at (0, -1).
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