NBT NBT Mathematics: Functions and Graphs 3

Question 1

The line y = mx + c has gradient −3 and passes through (1, 2). What is the equation?

Accepted Answer

y = −3x + 5

Answer

Using y − 2 = −3(x − 1): y = −3x + 3 + 2 = −3x + 5.

Question 2

A parabola has equation y = 2x² − 8x + 6. The axis of symmetry is:

Accepted Answer

x = 2

Answer

Axis of symmetry: x = −b/(2a) = 8/(2×2) = 2.

Question 3

The graph of f(x) = 2^x is reflected in the y-axis. What is the equation of the reflected graph?

Accepted Answer

f(x) = 2^(−x)

Answer

Reflection in y-axis replaces x with −x: f(x) = 2^(−x).

Question 4

On a graph, f(x) is a straight line that is neither increasing nor decreasing. Which type of function is this?

Accepted Answer

Constant function

Answer

A horizontal line represents a constant function where the output is the same for all x.

Question 5

Which function has an asymptote at y = 2?

Accepted Answer

f(x) = 3^x + 2

Answer

Exponential functions of the form a^x + c have horizontal asymptote y = c; here y = 2.

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