All Questions ⁺⁰238420 Questions

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Algebra

The graph of the invertible function y = f(x) is shown below.
If f(a)=b and f(b)=4, then what is the value of $a-b$?

Jyrgernry Apr 22, 2026

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The Custom Trophy Base

An artist is designing a unique geometric trophy base using a flat sheet of acrylic. The base is composed of several distinct sections that need to be cut from the same material. To calculate the total cost of materials, the artist needs to find the total read more ..

Jyrgerhry Apr 22, 2026

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The equation of the circle below can be expressed in the form x^2 + Ay^2 + Bx + Cy + D = 0. Find A+B+C+D.

AnswerscorrectIy Apr 22, 2026

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In the coordinate plane, one circle is centered at (0,-1), and another circle is centered at (-3,2), as shown below. The two circles are internally tangent.
The equation of the smaller circle can be expressed in the form x^2 + read more ..

AnswerscorrectIy Apr 22, 2026

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The graph of y = \frac{x + A}{Bx + C}, where $A,B,$ and $C$ are integers, is shown below. What is $A + B + C$?

Pythagorearn Apr 22, 2026

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The complete graph of f(x) is shown below, which consists of five line segments. Find the sum of all values of x that satisfy f(x) = x + 1.

Pythagorearn Apr 22, 2026

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The complete graph of f(x) is shown below, which consists of five line segments. Find the sum of all values of x that satisfy f(x) = 1.8.

Pythagorearn Apr 22, 2026

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The complete graph of f(x) is shown below.
Find the sum of all integers n for which the equation f(x)=n has exactly 6 solutions.

Pythagorearn Apr 22, 2026

Apr 21, 2026

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The complete graph of f(x) is shown below.
For a real number k, let g(k) be the number of solutions to the equation f(x)=k. What is the average of all distinct values in the range of g(k)?

gnistory Apr 21, 2026

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The complete graph of f(x) is shown below.
For a real number y, let g(y) be the number of solutions to the equation f(x)=y. What is the average of all distinct values in the range of g(y)?

gnistory Apr 21, 2026

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The graph of the quadratic function f(x) is shown below
Let g(x)=-f(x) and h(x)=f(-x). Let $a$ be the number of points where the graphs of $y=f(x)$ and $y=g(x)$ intersect, and let $b$ be the number of points where the graphs read more ..

gnistory Apr 21, 2026

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The graph of f(x)=ax^2+bx+c is shown below. What is the value of a+b+2c?

gnistory Apr 21, 2026

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The graph of f(x) is shown. What are the possible values of f(x) - x for -3 \le x \le 3? Enter your answer using interval notation.

Pythagorearn Apr 21, 2026

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The graph of G(x) is shown below. Compute G(G(G(G(G(1))))).

Pythagorearn Apr 21, 2026

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The graph of f(x) is shown below, where f(x) is a quadratic function. What is the sum of all $x$ such that $f(f(f(x)))=-3$ ?

Pythagorearn Apr 21, 2026

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For -1 \le x \le 1, let f(x) = 1 - \sqrt{1 - x^2}. The graph of f(x) is shown below.
The graphs of y = f(x) and y = f(x + 1) enclose a region. What is the area of that region, rounded to the nearest hundredth?

Pythagorearn Apr 21, 2026

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The graph of f(x) is shown below, which consists of five line segments.
Let a be the largest negative integer such that the function g(x) = f(x) + ax is invertible. Let $b$ be the smallest positive integer such that the function read more ..

kittykat Apr 21, 2026

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The graph of f(x) is shown below.
Mrs. Levans writes the number 3 on her pinky finger. She then applies $f$ to $3$ and writes the output on her ring finger. If Mrs. Levans continues this process of applying f and writing read more ..

kittykat Apr 21, 2026

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The graph of y = f(x) is shown below.
Find the sum of all integers x, 0\le x\le 8, such that f(x) > x.

kittykat Apr 21, 2026

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The graph of y = f(x) is shown below.
Find f(f(1))+f(f(2))+f(f(3))+\dots+f(f(8))+f(f(9)).

Boseo Apr 21, 2026

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The complete graph of the function f(x) is shown below. How many values of x satisfy f(f(x)) = 2?

Boseo Apr 21, 2026

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The graph of y = p(x) is shown below.
Find p(1.5).

Boseo Apr 21, 2026

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The graph of y = f(x) is shown below.
Find f(3).

cooIcooIcooI17 Apr 21, 2026

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The graph of y = f(x) is shown below, where f(x) = ax^2 + bx + c.
Find f(15).

cooIcooIcooI17 Apr 21, 2026

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The graph of y = f(x) is shown below.
The graphs of y = f(x) and y = f(x - 3) intersect at one point. What is the sum of the coordinates of that point?

cooIcooIcooI17 Apr 21, 2026

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