Exercises: Construct Linear and Exponential Functions

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Grade 9·21 problems·~30 min·Common Core Math - HS Functions·group·hsf-le-a-2

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Warm-Up: Review What You Know

A linear function passes through $(1, 5)$ and $(4, 14)$ . What is the slope?

A table shows $f(0) = 4$ , $f(1) = 12$ , $f(2) = 36$ . What is the common ratio?

The arithmetic sequence $3, 7, 11, 15, \ldots$ corresponds to which linear function?

$f(n) = 3n + 4$ for $n = 1, 2, 3, \ldots$

$f(n) = 4n - 1$ for $n = 1, 2, 3, \ldots$

$f(n) = 3 \cdot 4^{n-1}$ for $n = 1, 2, 3, \ldots$

$f(n) = 4n + 3$ for $n = 1, 2, 3, \ldots$

A linear function passes through $(2, 7)$ and $(5, 16)$ .

Find the y-intercept $b$ (the value of the function when $x = 0$ ).

The arithmetic sequence $5, 8, 11, 14, \ldots$ corresponds to a linear function $f(n) = mn + b$ for positive integers $n$ .

What is the value of $b$ (the y-intercept)?

An exponential function passes through $(1, 6)$ and $(3, 54)$ .

Find the base $b$ of the function $f(x) = a \cdot b^x$ .

A function $g(x)$ has the values $g(2) = 12$ , $g(3) = 36$ , $g(4) = 108$ .

Find the initial value $a$ for the exponential function $g(x) = a \cdot b^x$ .

A graph of a linear function passes through integer coordinate points $(1, 5)$ and $(3, 9)$ . Which function matches the graph?

$f(x) = 2x + 3$

$f(x) = 3x + 2$

$f(x) = 2x + 5$

$f(x) = 4x + 1$

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