Quiz on Lessons 1.3-1.4

Information about the function g(x) is given in the table. The function g(x) is defined for all real numbers.

Which of the following statements is guaranteed to be true about

g(x)?

Luna, Anika, and Mia are studying for their math test. They come across a function whose values are given at selected 𝒙-values in the table below. They notice that the function’s concavity does not change. Can you help them determine if the function is concave up or concave down? Justify your answer.

The values of a function are given at selected 𝒙-values in the table below. The function’s concavity does not change. Determine if the function is concave up or concave down. Justify your answer.

Anika, Grace, and David are playing a game of 'Guess the Function'. They have a table that gives values of a mysterious function ℎ for selected values of 𝑥.

They discovered that if the function f is linear, they can predict the next value. Can you help them guess what the value of f(32) would be if the function is indeed linear?

Abigail, Aiden, and William are on a treasure hunt. They found a map with a strange equation h(x) = -7x + 5. They need to find the average rate of change of this function on -5 $$\le$$ x $$\le$$ 10 to unlock the next clue. Can you help them?

Find the average rate of change of the function g(x) = $$-2x^2+5x\ -3$$ on the interval [2, 5].

Benjamin, Maya, and Mia are studying quadratic functions. They come across a function 𝒈 and notice some interesting patterns.

They find that the average rate of change is -6 on the interval 0 $$\le x\le$$ 5. They also observe that the average rate of change is -2 on the interval 5 $$\le x\le$$ 10. They are now curious to know what would be the average rate of change of 𝑔 on the interval 20 $$\le x\le25$$ . Can you help them figure it out?

What is the rate of change of the average rates of change for each function over consecutive equal-length intervals?

y = -0.5 x

Find the leading coefficient and degree of

$$f\left(x\right)\ =-10x^3-4x-3x^4+3$$

Aria, David, and William are on a treasure hunt. They found a mysterious scroll with a riddle:

$$g\left(x\right)\ =\ x\left(-3x-1\right)\left(2x+3\right)^3$$

They believe solving it will lead them to the treasure. Can you help them find the leading coefficient and the degree of this riddle?