Back to Tutor Intake Assessment: Construct linear and exponential functions

HSF.LE.A.2 Tutor Intake -- Constructing Linear and Exponential Functions

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Grade 9·11 problems·~14 min·Common Core Math - HS Functions·group·hsf-le-a-2

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Concepts

A linear function passes through the points $(1, 5)$ and $(4, 14)$ .

What is the slope of this function?

An exponential function passes through $(0, 5)$ and $(1, 15)$ .
Which equation represents this function?

$f(x) = 5 \cdot 3^x$

$f(x) = 15 \cdot 5^x$

$f(x) = 5 \cdot 10^x$

$f(x) = 3x + 5$

A student examines this table:

$x$	$f(x)$
0	6
1	9
2	12
3	15

The student correctly identifies the relationship as linear. Which feature of
the table led to this conclusion?

The outputs increase by the same amount each step (constant differences).

The outputs are multiplied by the same factor each step (constant ratios).

The first output is 6, which equals $2 \times 3$ , so the slope is 2.

The input values increase by 1 each step.

Procedures

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

What is the $y$ -intercept of this function?

A linear function passes through $(3, 10)$ and $(7, 18)$ .
Which equation correctly represents this function?

$f(x) = 2x + 4$

$f(x) = 2x + 10$

$f(x) = 8x + 10$

$f(x) = 4x - 2$

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

What is the base $b$ of this function?

An exponential function passes through $(1, 6)$ and $(3, 54)$ , with base $b = 3$ .

What is the initial value $a$ ?

$a = 2$

$a = 6$

$a = 18$

$a = 3$

A student looks at this table and must decide whether it is linear or exponential:

$x$	$g(x)$
0	8
1	12
2	18
3	27

Which equation correctly represents this table?

$g(x) = 8 \cdot (1.5)^x$

$g(x) = 4x + 8$

$g(x) = 8 \cdot 12^x$

$g(x) = 8 + 4x$

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