Question 1
The function \(f(x) = ax + b\) satisfies \(f(3) = 10\) and \(f(-1) = -6\). What is the value of \(a + b\)?
Hard - Quiz 1
Think you've mastered linear functions? These problems demand careful reasoning about perpendicular lines, function behavior, and multi-constraint scenarios.
Question 1 of 5
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Answer question 1 to unlock
Line \(\ell\) passes through \((1, 5)\) and is perpendicular to the line \(2x + 3y = 12\). What is the \(y\)-intercept of line \(\ell\)?
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Answer question 2 to unlock
A company offers two salary structures for a sales position. Structure A pays a monthly base of $2,400 plus $60 per unit sold. Structure B pays no base but $120 per unit sold. A salesperson who picks Structure A will earn more than one who picks Structure B as long as they sell fewer than how many units per month?
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Answer question 3 to unlock
The linear function \(g\) is defined so that \(g(x + 2) = g(x) + 8\) for all values of \(x\). If \(g(0) = 3\), what is \(g(7)\)?
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Answer question 4 to unlock
A tank is being filled at a constant rate. At 8:00 AM it holds 40 liters, and at 8:30 AM it holds 70 liters. A second tank starts empty at 8:00 AM and fills at a constant rate of 3 liters per minute. After how many minutes will both tanks hold the same amount of water?