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Algebraic Reasoning and Functions Flashcards

6 cards from real TSI practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. A rectangular garden has a length that is 5 feet longer than its width, w. The area of the garden is 104 square feet. Which of the following equations can be used to find the width of the garden?

    Answer: w(w + 5) = 104

    The area of a rectangle is calculated by multiplying its length by its width. In this scenario, the width is 'w' and the length is 'w + 5'. Therefore, the equation representing the area is w multiplied by (w + 5), which equals 104.

  2. If f(x) = 3x^2 - 4x + 1, what is the value of f(-2)?

    Answer: 21

    To evaluate f(-2), substitute -2 for every x in the function: f(-2) = 3(-2)^2 - 4(-2) + 1. This simplifies to 3(4) + 8 + 1, which is 12 + 8 + 1 = 21.

  3. Which of the following is equivalent to the expression (2x - 3)(x + 4)?

    Answer: 2x^2 + 5x - 12

    To expand the expression, use the FOIL method (First, Outer, Inner, Last). First: (2x)(x) = 2x^2. Outer: (2x)(4) = 8x. Inner: (-3)(x) = -3x. Last: (-3)(4) = -12. Combine the like terms (8x - 3x = 5x) to get the final expression: 2x^2 + 5x - 12.

  4. A cell phone plan costs $20 per month plus $0.15 for each text message sent. Which function can be used to find the total monthly cost, C(t), for sending 't' text messages?

    Answer: C(t) = 20 + 0.15t

    The total cost is the sum of the fixed monthly fee and the variable cost based on the number of text messages. The fixed fee is $20. The variable cost is $0.15 multiplied by the number of texts, 't'. Therefore, the function is C(t) = 20 + 0.15t.

  5. If 4(x - 2) + 5x = 3(x + 4), what is the value of x?

    Answer: x = 10/3

    First, distribute the numbers outside the parentheses: 4x - 8 + 5x = 3x + 12. Combine like terms on the left side: 9x - 8 = 3x + 12. Subtract 3x from both sides: 6x - 8 = 12. Add 8 to both sides: 6x = 20. Finally, divide by 6: x = 20/6, which simplifies to 10/3.

  6. The graph of a quadratic function opens downwards and has a vertex at (3, -2). Which of the following could be the equation of the function?

    Answer: y = -(x - 3)^2 - 2

    A quadratic function in vertex form is y = a(x - h)^2 + k, where (h, k) is the vertex. Since the vertex is (3, -2), h=3 and k=-2. The parabola opens downwards, which means the leading coefficient 'a' must be negative. Therefore, the equation must be in the form y = -(x - 3)^2 - 2.